diff --git a/Project.toml b/Project.toml
index 62644e446997..e02df96a9029 100644
--- a/Project.toml
+++ b/Project.toml
@@ -31,7 +31,7 @@ AlgebraicSolving = "0.4.11"
 Distributed = "1.6"
 DocStringExtensions = "0.8, 0.9"
 GAP = "0.10.2"
-Hecke = "0.29.0"
+Hecke = "0.30.0"
 JSON = "^0.20, ^0.21"
 JSON3 = "1.13.2"
 LazyArtifacts = "1.6"
diff --git a/experimental/FTheoryTools/src/auxiliary.jl b/experimental/FTheoryTools/src/auxiliary.jl
index a11ee072b3a9..127c3601715a 100644
--- a/experimental/FTheoryTools/src/auxiliary.jl
+++ b/experimental/FTheoryTools/src/auxiliary.jl
@@ -35,10 +35,10 @@ function _ambient_space(base::NormalToricVariety, fiber_amb_space::NormalToricVa
   
   # Compute divisor group and the class group of a_space
   a_space_divisor_group = free_abelian_group(nrows(a_rays))
-  a_space_class_group = free_abelian_group(ncols(b_grades) + rank(class_group(fiber_amb_space)))
+  a_space_class_group = free_abelian_group(ncols(b_grades) + torsion_free_rank(class_group(fiber_amb_space)))
   
   # Compute grading of Cox ring of a_space
-  a_space_grading = zero_matrix(ZZ, rank(a_space_divisor_group), rank(a_space_class_group))
+  a_space_grading = zero_matrix(ZZ, torsion_free_rank(a_space_divisor_group), torsion_free_rank(a_space_class_group))
   a_space_grading[1:nrows(b_grades), 1:ncols(b_grades)] = b_grades
   a_space_grading[1+nrows(b_rays):nrows(b_rays) + nrows(f_grades), 1+ncols(b_grades):ncols(b_grades) + ncols(f_grades)] = f_grades
   a_space_grading[1+nrows(b_rays), 1:ncols(D1_coeffs)] = D1_coeffs
diff --git a/experimental/GModule/Cohomology.jl b/experimental/GModule/Cohomology.jl
index 183f4d1b6707..5111d967f340 100644
--- a/experimental/GModule/Cohomology.jl
+++ b/experimental/GModule/Cohomology.jl
@@ -474,7 +474,10 @@ export action, cohomology_group, extension, pc_group_with_isomorphism
 export induce, is_consistent, istwo_cocycle, all_extensions
 export split_extension, extension_with_abelian_kernel
 
-Oscar.dim(C::GModule) = rank(C.M)
+_rank(M::FinGenAbGroup) = torsion_free_rank(M)
+_rank(M) = rank(M)
+
+Oscar.dim(C::GModule) = _rank(C.M)
 Oscar.base_ring(C::GModule) = base_ring(C.M)
 Oscar.group(C::GModule) = C.G
 
diff --git a/experimental/GModule/GaloisCohomology.jl b/experimental/GModule/GaloisCohomology.jl
index 7a8e8e928798..13d5891c181e 100644
--- a/experimental/GModule/GaloisCohomology.jl
+++ b/experimental/GModule/GaloisCohomology.jl
@@ -542,7 +542,7 @@ Follows Debeerst rather closely...
 function debeerst(M::FinGenAbGroup, sigma::Map{FinGenAbGroup, FinGenAbGroup})
   @assert domain(sigma) == codomain(sigma) == M
   @assert all(x->sigma(sigma(x)) == x, gens(M))
-  @assert is_free(M) && rank(M) == ngens(M)
+  @assert is_free(M) && torsion_free_rank(M) == ngens(M)
 
   K, mK = kernel(id_hom(M)+sigma)
   fl, mX = has_complement(mK)
@@ -557,8 +557,8 @@ function debeerst(M::FinGenAbGroup, sigma::Map{FinGenAbGroup, FinGenAbGroup})
 
   _K, _mK = snf(K)
   _S, _mS = snf(S)
-  @assert is_trivial(_S) || rank(_S) == ngens(_S) 
-  @assert rank(_K) == ngens(_K) 
+  @assert is_trivial(_S) || torsion_free_rank(_S) == ngens(_S) 
+  @assert torsion_free_rank(_K) == ngens(_K) 
 
   m = matrix(FinGenAbGroupHom(_mS * mSK * inv((_mK))))
   # elt in S * m = elt in K
@@ -1912,7 +1912,7 @@ function shrink(C::GModule{PermGroup, FinGenAbGroup}, attempts::Int = 10)
       o = Oscar.orbit(q, rand(gens(q.M)))
       if length(o) == order(group(q))
         s, ms = sub(q.M, collect(o), false)
-        if rank(s) == length(o)
+        if torsion_free_rank(s) == length(o)
           q, _mq = quo(q, ms, false)
           if first
             mq = _mq
diff --git a/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/attributes.jl b/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/attributes.jl
index 515b816b5f58..f60dfe25bdf2 100644
--- a/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/attributes.jl
+++ b/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/attributes.jl
@@ -198,7 +198,7 @@ julia> coordinate_names(antv)
 ```
 """
 @attr Vector{String} function coordinate_names(v::NormalToricVarietyType)
-    return ["x$(i)" for i in 1:rank(torusinvariant_weil_divisor_group(v))]
+    return ["x$(i)" for i in 1:torsion_free_rank(torusinvariant_weil_divisor_group(v))]
 end
 
 
@@ -679,8 +679,8 @@ julia> torusinvariant_prime_divisors(p2)
 @attr Vector{ToricDivisor} function torusinvariant_prime_divisors(v::NormalToricVarietyType)
     ti_divisors = torusinvariant_weil_divisor_group(v)
     prime_divisors = ToricDivisor[]
-    for i in 1:rank(ti_divisors)
-        coeffs = zeros(Int, rank(ti_divisors))
+    for i in 1:torsion_free_rank(ti_divisors)
+        coeffs = zeros(Int, torsion_free_rank(ti_divisors))
         coeffs[i] = 1
         push!(prime_divisors, toric_divisor(v, coeffs))
     end
@@ -756,7 +756,7 @@ Map
     number_of_cones = size(max_cones)[1]
     
     # compute quantities needed to construct the matrices
-    rc = rank(character_lattice(v))
+    rc = torsion_free_rank(character_lattice(v))
     number_ray_is_part_of_max_cones = [length(max_cones[:, k].s) for k in 1:number_of_rays]
     s = sum(number_ray_is_part_of_max_cones)
     cones_ray_is_part_of = [filter(x -> max_cones[x, r], 1:number_of_cones) for r in 1:number_of_rays]
@@ -784,7 +784,7 @@ Map
     end
     
     # compute the matrix for mapping to torusinvariant Weil divisors
-    map_to_weil_divisors = zero_matrix(ZZ, number_of_cones * rc, rank(torusinvariant_weil_divisor_group(v)))
+    map_to_weil_divisors = zero_matrix(ZZ, number_of_cones * rc, torsion_free_rank(torusinvariant_weil_divisor_group(v)))
     for i in 1:number_of_rays
         map_to_weil_divisors[(cones_ray_is_part_of[i][1]-1)*rc+1:cones_ray_is_part_of[i][1]*rc, i] = [ZZRingElem(-c) for c in fan_rays[:, i]]
     end
diff --git a/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/properties.jl b/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/properties.jl
index 99582ec6ce76..5ff27f7096bc 100644
--- a/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/properties.jl
+++ b/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/properties.jl
@@ -68,7 +68,7 @@ true
     if is_projective(v) == false
         return false
     end
-    if rank(class_group(v)) > 1
+    if torsion_free_rank(class_group(v)) > 1
         return false
     end
     w = [[Int(x) for x in transpose(g.coeff)] for g in gens(class_group(v))]
diff --git a/src/AlgebraicGeometry/ToricVarieties/ToricDivisors/constructors.jl b/src/AlgebraicGeometry/ToricVarieties/ToricDivisors/constructors.jl
index b6f80358aa1d..1c90960f5540 100644
--- a/src/AlgebraicGeometry/ToricVarieties/ToricDivisors/constructors.jl
+++ b/src/AlgebraicGeometry/ToricVarieties/ToricDivisors/constructors.jl
@@ -68,7 +68,7 @@ Torus-invariant, non-prime divisor on a normal toric variety
 ```
 """
 function divisor_of_character(v::NormalToricVarietyType, character::Vector{T}) where {T <: IntegerUnion}
-    r = rank(character_lattice(v))
+    r = torsion_free_rank(character_lattice(v))
     @req length(character) == r "Character must consist of $r integers"
     f = map_from_character_lattice_to_torusinvariant_weil_divisor_group(v)
     char = sum(character .* gens(domain(f)))
diff --git a/src/AlgebraicGeometry/ToricVarieties/ToricMorphisms/attributes.jl b/src/AlgebraicGeometry/ToricVarieties/ToricMorphisms/attributes.jl
index f9fcd02bec27..04694ec3b961 100644
--- a/src/AlgebraicGeometry/ToricVarieties/ToricMorphisms/attributes.jl
+++ b/src/AlgebraicGeometry/ToricVarieties/ToricMorphisms/attributes.jl
@@ -73,7 +73,7 @@ Map
     cod = codomain(tm)
     cod_rays = matrix(ZZ, rays(cod))
     images = matrix(ZZ, rays(d)) * matrix(grid_morphism(tm))
-    mapping_matrix = matrix(ZZ, zeros(ZZ, rank(torusinvariant_weil_divisor_group(cod)), 0))
+    mapping_matrix = matrix(ZZ, zeros(ZZ, torsion_free_rank(torusinvariant_weil_divisor_group(cod)), 0))
     for i in 1:nrows(images)
       v = [images[i,k] for k in 1:ncols(images)]
       j = findfirst(x -> x == true, [(v in maximal_cones(cod)[j]) for j in 1:n_maximal_cones(cod)])
diff --git a/src/AlgebraicGeometry/ToricVarieties/ToricMorphisms/constructors.jl b/src/AlgebraicGeometry/ToricVarieties/ToricMorphisms/constructors.jl
index b679f8db0867..d1b84870a325 100644
--- a/src/AlgebraicGeometry/ToricVarieties/ToricMorphisms/constructors.jl
+++ b/src/AlgebraicGeometry/ToricVarieties/ToricMorphisms/constructors.jl
@@ -109,10 +109,10 @@ function toric_morphism(domain::NormalToricVarietyType, grid_morphism::FinGenAbG
     @req (nrows(matrix(grid_morphism)) > 0 && ncols(matrix(grid_morphism)) > 0) "The mapping matrix must not be empty"
 
     # check for a well-defined map
-    @req nrows(matrix(grid_morphism)) == rank(character_lattice(domain)) "The number of rows of the mapping matrix must match the rank of the character lattice of the domain toric variety"
+    @req nrows(matrix(grid_morphism)) == torsion_free_rank(character_lattice(domain)) "The number of rows of the mapping matrix must match the rank of the character lattice of the domain toric variety"
 
     # compute the morphism
-    @req ncols(matrix(grid_morphism)) == rank(character_lattice(codomain)) "The number of columns of the mapping matrix must match the rank of the character lattice of the codomain toric variety"
+    @req ncols(matrix(grid_morphism)) == torsion_free_rank(character_lattice(codomain)) "The number of columns of the mapping matrix must match the rank of the character lattice of the codomain toric variety"
     if check
       codomain_cones = maximal_cones(codomain)
       image_cones = [positive_hull(matrix(ZZ, rays(c)) * matrix(grid_morphism)) for c in maximal_cones(domain)]
@@ -144,7 +144,7 @@ Toric morphism
 ```
 """
 function toric_identity_morphism(variety::NormalToricVarietyType)
-    r = rank(character_lattice(variety))
+    r = torsion_free_rank(character_lattice(variety))
     identity_matrix = matrix(ZZ, [[if i==j 1 else 0 end for j in 1:r] for i in 1:r])
     grid_morphism = hom(character_lattice(variety), character_lattice(variety), identity_matrix)
     return ToricMorphism(variety, grid_morphism, variety)
diff --git a/src/AlgebraicGeometry/ToricVarieties/cohomCalg/VanishingSets/constructors.jl b/src/AlgebraicGeometry/ToricVarieties/cohomCalg/VanishingSets/constructors.jl
index 35fd82e0a001..5dc2de519646 100644
--- a/src/AlgebraicGeometry/ToricVarieties/cohomCalg/VanishingSets/constructors.jl
+++ b/src/AlgebraicGeometry/ToricVarieties/cohomCalg/VanishingSets/constructors.jl
@@ -7,7 +7,7 @@
     ps::Vector{Polyhedron{QQFieldElem}}
     cis::Vector{Int}
     function ToricVanishingSet(toric_variety::NormalToricVarietyType, ps::Vector{Polyhedron{QQFieldElem}}, cis::Vector{Int})
-        if !all(p -> ambient_dim(p) == rank(picard_group(toric_variety)), ps)
+        if !all(p -> ambient_dim(p) == torsion_free_rank(picard_group(toric_variety)), ps)
             throw(ArgumentError("The ambient dimensions of the polyhedra must match the rank as the picard group of the toric variety"))
         end
         if !all(i -> 0 <= i <= dim(toric_variety), cis)
diff --git a/src/AlgebraicGeometry/ToricVarieties/cohomCalg/auxiliary.jl b/src/AlgebraicGeometry/ToricVarieties/cohomCalg/auxiliary.jl
index 9e65f0d505e7..ab3efcfb6f2b 100644
--- a/src/AlgebraicGeometry/ToricVarieties/cohomCalg/auxiliary.jl
+++ b/src/AlgebraicGeometry/ToricVarieties/cohomCalg/auxiliary.jl
@@ -29,7 +29,7 @@ function command_string(v::NormalToricVarietyType, c::Vector{ZZRingElem})
     # Join and return
     return join(string_list, ";")
 end
-command_string(v::NormalToricVarietyType) = command_string(v, [ZZRingElem(0) for i in 1:rank(picard_group(v))])
+command_string(v::NormalToricVarietyType) = command_string(v, [ZZRingElem(0) for i in 1:torsion_free_rank(picard_group(v))])
 
 
 
diff --git a/src/Modules/ModulesGraded.jl b/src/Modules/ModulesGraded.jl
index f11731edbbd0..a7d257e9eb96 100644
--- a/src/Modules/ModulesGraded.jl
+++ b/src/Modules/ModulesGraded.jl
@@ -3077,8 +3077,7 @@ end
 function _regularity_bound(M::SubquoModule)
   @assert is_graded(M) "module must be graded"
   S = base_ring(M)
-  G = grading_group(S)
-  @assert is_free(G) && isone(rank(G)) "base ring must be ZZ-graded"
+  @assert is_z_graded(S) "base ring must be ZZ-graded"
   @assert all(x->degree(Int, x; check=false) >= 0, gens(S)) "base ring variables must be non-negatively graded"
   res = free_resolution(M)
   result = maximum((x->degree(Int, x; check=false)).(gens(res[0])))
diff --git a/src/Rings/mpoly-graded.jl b/src/Rings/mpoly-graded.jl
index a779894feaec..479f1d0ae0a0 100644
--- a/src/Rings/mpoly-graded.jl
+++ b/src/Rings/mpoly-graded.jl
@@ -231,7 +231,8 @@ is_standard_graded(::MPolyRing) = false
 Return `true` if `R` is $\mathbb Z$-graded, `false` otherwise.
 
 !!! note
-    Writing `G = grading_group(R)`, we say that `R` is $\mathbb Z$-graded if `is_free(G) && ngens(G) == rank(G) == 1` evaluates to `true`.
+    Writing `G = grading_group(R)`, we say that `R` is $\mathbb Z$-graded if
+    `G` is free abelian of rank `1`, and `ngens(G) == 1`.
 
 # Examples
 ```jldoctest
@@ -245,7 +246,7 @@ true
 function is_z_graded(R::MPolyDecRing)
   is_graded(R) || return false
   A = grading_group(R)
-  return ngens(A) == 1 && rank(A) == 1 && is_free(A)
+  return ngens(A) == 1 && torsion_free_rank(A) == 1 && is_free(A)
 end
 
 is_z_graded(::MPolyRing) = false
@@ -256,7 +257,8 @@ is_z_graded(::MPolyRing) = false
 Return `true` if `R` is $\mathbb Z^m$-graded for some $m$, `false` otherwise.
 
 !!! note
-    Writing `G = grading_group(R)`, we say that `R` is $\mathbb Z^m$-graded if `is_free(G) && ngens(G) == rank(G) == m` evaluates to `true`.
+    Writing `G = grading_group(R)`, we say that `R` is $\mathbb Z^m$-graded
+    `G` is free abelian of rank `m`, and `ngens(G) == m`.
 
 # Examples
 ```jldoctest
@@ -295,7 +297,7 @@ false
 function is_zm_graded(R::MPolyDecRing)
   is_graded(R) || return false
   A = grading_group(R)
-  return is_free(A) && ngens(A) == rank(A)
+  return is_free(A) && ngens(A) == torsion_free_rank(A)
 end
 
 is_zm_graded(::MPolyRing) = false
@@ -340,7 +342,7 @@ false
   is_graded(R) || return false
   G = grading_group(R)
   is_free(G) || return false
-  if ngens(G) == rank(G)
+  if ngens(G) == torsion_free_rank(G)
     W = reduce(vcat, [x.coeff for x = R.d])
     if is_positive_grading_matrix(transpose(W))
        return true
diff --git a/src/imports.jl b/src/imports.jl
index 9c7ff7555fb8..bdb686fc6718 100644
--- a/src/imports.jl
+++ b/src/imports.jl
@@ -195,4 +195,10 @@ import Hecke:
   primitive_element,
   QQBar
 
+# temporary workaround, see https://github.com/thofma/Hecke.jl/pull/1224
+if !isdefined(Hecke, :torsion_free_rank)
+  torsion_free_rank(A::FinGenAbGroup) = rank(A)
+  export torsion_free_rank
+end
+
 import cohomCalg_jll
diff --git a/test/AlgebraicGeometry/ToricVarieties/affine_normal_varieties.jl b/test/AlgebraicGeometry/ToricVarieties/affine_normal_varieties.jl
index 019216a78672..b412a3037c33 100644
--- a/test/AlgebraicGeometry/ToricVarieties/affine_normal_varieties.jl
+++ b/test/AlgebraicGeometry/ToricVarieties/affine_normal_varieties.jl
@@ -18,10 +18,10 @@
     @test dim(cone(antv)) == 2
     @test length(affine_open_covering(antv)) == 1
     @test length(gens(toric_ideal(antv))) == 1
-    @test rank(torusinvariant_weil_divisor_group(antv)) == 2
-    @test rank(character_lattice(antv)) == 2
-    @test rank(domain(map_from_character_lattice_to_torusinvariant_weil_divisor_group(antv))) == 2
-    @test rank(codomain(map_from_character_lattice_to_torusinvariant_weil_divisor_group(antv))) == 2
+    @test torsion_free_rank(torusinvariant_weil_divisor_group(antv)) == 2
+    @test torsion_free_rank(character_lattice(antv)) == 2
+    @test torsion_free_rank(domain(map_from_character_lattice_to_torusinvariant_weil_divisor_group(antv))) == 2
+    @test torsion_free_rank(codomain(map_from_character_lattice_to_torusinvariant_weil_divisor_group(antv))) == 2
     @test elementary_divisors(codomain(map_from_torusinvariant_weil_divisor_group_to_class_group(antv))) == [ 2 ]
     @test elementary_divisors(class_group(antv)) == [ 2 ]
     @test ngens(cox_ring(antv)) == 2
diff --git a/test/AlgebraicGeometry/ToricVarieties/del_pezzo_surfaces.jl b/test/AlgebraicGeometry/ToricVarieties/del_pezzo_surfaces.jl
index 4fa34e96a80d..b51f03cbd1f2 100644
--- a/test/AlgebraicGeometry/ToricVarieties/del_pezzo_surfaces.jl
+++ b/test/AlgebraicGeometry/ToricVarieties/del_pezzo_surfaces.jl
@@ -23,8 +23,8 @@
   
   @testset "Basic attributes of dP1" begin
     @test length(torusinvariant_prime_divisors(dP1)) == 4
-    @test rank(torusinvariant_cartier_divisor_group(dP1)) == 4
-    @test rank(picard_group(dP1)) == 2
+    @test torsion_free_rank(torusinvariant_cartier_divisor_group(dP1)) == 4
+    @test torsion_free_rank(picard_group(dP1)) == 2
     @test transpose(matrix(ZZ,rays(dP1))) == matrix(map_from_character_lattice_to_torusinvariant_weil_divisor_group(dP1))
     @test domain(map_from_character_lattice_to_torusinvariant_weil_divisor_group(dP1)) == character_lattice(dP1)
     @test codomain(map_from_character_lattice_to_torusinvariant_weil_divisor_group(dP1)) == torusinvariant_weil_divisor_group(dP1)
@@ -44,8 +44,8 @@
   
   @testset "Basic attributes of dP2" begin
     @test length(torusinvariant_prime_divisors(dP2)) == 5
-    @test rank(torusinvariant_cartier_divisor_group(dP2)) == 5
-    @test rank(picard_group(dP2)) == 3
+    @test torsion_free_rank(torusinvariant_cartier_divisor_group(dP2)) == 5
+    @test torsion_free_rank(picard_group(dP2)) == 3
     @test transpose(matrix(ZZ,rays(dP2))) == matrix(map_from_character_lattice_to_torusinvariant_weil_divisor_group(dP2))
     @test domain(map_from_character_lattice_to_torusinvariant_weil_divisor_group(dP2)) == character_lattice(dP2)
     @test codomain(map_from_character_lattice_to_torusinvariant_weil_divisor_group(dP2)) == torusinvariant_weil_divisor_group(dP2)
@@ -65,8 +65,8 @@
   
   @testset "Basic attributes of dP3" begin
     @test length(torusinvariant_prime_divisors(dP3)) == 6
-    @test rank(torusinvariant_cartier_divisor_group(dP3)) == 6
-    @test rank(picard_group(dP3)) == 4
+    @test torsion_free_rank(torusinvariant_cartier_divisor_group(dP3)) == 6
+    @test torsion_free_rank(picard_group(dP3)) == 4
     @test transpose(matrix(ZZ,rays(dP3))) == matrix(map_from_character_lattice_to_torusinvariant_weil_divisor_group(dP3))
     @test domain(map_from_character_lattice_to_torusinvariant_weil_divisor_group(dP3)) == character_lattice(dP3)
     @test codomain(map_from_character_lattice_to_torusinvariant_weil_divisor_group(dP3)) == torusinvariant_weil_divisor_group(dP3)
diff --git a/test/AlgebraicGeometry/ToricVarieties/hirzebruch_surfaces.jl b/test/AlgebraicGeometry/ToricVarieties/hirzebruch_surfaces.jl
index 56d0675c66ae..1300caab0ab5 100644
--- a/test/AlgebraicGeometry/ToricVarieties/hirzebruch_surfaces.jl
+++ b/test/AlgebraicGeometry/ToricVarieties/hirzebruch_surfaces.jl
@@ -34,17 +34,17 @@
     @test betti_number(F5, 4) == 1
     @test length(affine_open_covering(F5)) == 4
     @test dim(polyhedral_fan(F5)) == 2
-    @test rank(torusinvariant_weil_divisor_group(F5)) == 4
-    @test rank(character_lattice(F5)) == 2
+    @test torsion_free_rank(torusinvariant_weil_divisor_group(F5)) == 4
+    @test torsion_free_rank(character_lattice(F5)) == 2
     @test ngens(cox_ring(F5)) == 4
     @test length(stanley_reisner_ideal(F5).gens) == 2
     @test length(irrelevant_ideal(F5).gens) == 4
     @test dim(nef_cone(F5)) == 2
     @test dim(mori_cone(F5)) == 2
-    @test rank(domain(map_from_character_lattice_to_torusinvariant_weil_divisor_group(F5))) == 2
-    @test rank(codomain(map_from_character_lattice_to_torusinvariant_weil_divisor_group(F5))) == 4
-    @test rank(class_group(F5)) == 2
-    @test rank(codomain(map_from_torusinvariant_weil_divisor_group_to_class_group(F5))) == 2
+    @test torsion_free_rank(domain(map_from_character_lattice_to_torusinvariant_weil_divisor_group(F5))) == 2
+    @test torsion_free_rank(codomain(map_from_character_lattice_to_torusinvariant_weil_divisor_group(F5))) == 4
+    @test torsion_free_rank(class_group(F5)) == 2
+    @test torsion_free_rank(codomain(map_from_torusinvariant_weil_divisor_group_to_class_group(F5))) == 2
     @test transpose(matrix(ZZ,rays(F5))) == matrix(map_from_character_lattice_to_torusinvariant_weil_divisor_group(F5))
     @test domain(map_from_character_lattice_to_torusinvariant_weil_divisor_group(F5)) == character_lattice(F5)
     @test codomain(map_from_character_lattice_to_torusinvariant_weil_divisor_group(F5)) == torusinvariant_weil_divisor_group(F5)
diff --git a/test/AlgebraicGeometry/ToricVarieties/normal_toric_varieties.jl b/test/AlgebraicGeometry/ToricVarieties/normal_toric_varieties.jl
index b9472c48a085..f5de0c6d67c0 100644
--- a/test/AlgebraicGeometry/ToricVarieties/normal_toric_varieties.jl
+++ b/test/AlgebraicGeometry/ToricVarieties/normal_toric_varieties.jl
@@ -9,8 +9,8 @@
   @testset "Basic properties" begin
     @test is_complete(ntv) == true
     @test is_projective_space(ntv) == false
-    @test rank(torusinvariant_cartier_divisor_group(ntv)) == 4
-    @test rank(domain(map_from_torusinvariant_cartier_divisor_group_to_torusinvariant_weil_divisor_group(ntv))) == 4
+    @test torsion_free_rank(torusinvariant_cartier_divisor_group(ntv)) == 4
+    @test torsion_free_rank(domain(map_from_torusinvariant_cartier_divisor_group_to_torusinvariant_weil_divisor_group(ntv))) == 4
     @test is_complete(ntv2) == true
     @test length(ntv3) == 1
     @test is_projective_space(ntv3[1]) == true
diff --git a/test/AlgebraicGeometry/ToricVarieties/projectivization.jl b/test/AlgebraicGeometry/ToricVarieties/projectivization.jl
index 49e54cc85bcd..9191ac211eb3 100644
--- a/test/AlgebraicGeometry/ToricVarieties/projectivization.jl
+++ b/test/AlgebraicGeometry/ToricVarieties/projectivization.jl
@@ -7,7 +7,7 @@
       X = projectivization(D0, Da)
       @test is_smooth(X) == true
       @test (a < 2) == is_fano(X)
-      @test rank(picard_group(X)) == 2
+      @test torsion_free_rank(picard_group(X)) == 2
       @test integrate(cohomology_class(anticanonical_divisor(X))^dim(X)) == integrate(cohomology_class(anticanonical_divisor(hirzebruch_surface(NormalToricVariety, a)))^2)
     end
   end
@@ -24,13 +24,13 @@
   D2 = toric_divisor(P2, [0,2,0])
   X3_P2 = projectivization(D0, D2)
   @testset "Test of some Fano projective bundles of dimension 3 over P2" begin
-    @test rank(picard_group(X1_P2)) == 2
+    @test torsion_free_rank(picard_group(X1_P2)) == 2
     @test is_fano(X1_P2) == true
     @test integrate(cohomology_class(anticanonical_divisor(X1_P2))^dim(X1_P2)) == 54
-    @test rank(picard_group(X2_P2)) == 2
+    @test torsion_free_rank(picard_group(X2_P2)) == 2
     @test is_fano(X2_P2) == true
     @test integrate(cohomology_class(anticanonical_divisor(X2_P2))^dim(X2_P2)) == 56
-    @test rank(picard_group(X3_P2)) == 2
+    @test torsion_free_rank(picard_group(X3_P2)) == 2
     @test is_fano(X3_P2) == true
     @test integrate(cohomology_class(anticanonical_divisor(X3_P2))^dim(X3_P2)) == 62
   end
@@ -43,11 +43,11 @@
   l1_F1 = toric_line_bundle(F1, [0,1])
   X2_F1 = projectivization(toric_line_bundle(F1, [0,0]), l1_F1)
   @testset "Test of some Fano projective bundles of dimension 3 over F1" begin
-    @test rank(picard_group(X1_F1)) == 3
+    @test torsion_free_rank(picard_group(X1_F1)) == 3
     @test is_fano(X1_F1) == true
     @test integrate(cohomology_class(anticanonical_divisor(X1_F1))^dim(X1_F1)) == 48
     @test integrate(cohomology_class(l1_F1)^2) == 1
-    @test rank(picard_group(X2_F1)) == 3
+    @test torsion_free_rank(picard_group(X2_F1)) == 3
     @test is_fano(X2_F1) == true
     @test integrate(cohomology_class(anticanonical_divisor(X2_F1))^dim(X2_F1)) == 50
   end
@@ -61,13 +61,13 @@
   X2_P1xP1 = projectivization(O10, O10)
   X3_P1xP1 = projectivization(O00, O11)
   @testset "Test of some Fano projective bundles of dimension 3 over P1 * P1" begin
-    @test rank(picard_group(X1_P1xP1)) == 3
+    @test torsion_free_rank(picard_group(X1_P1xP1)) == 3
     @test is_fano(X1_P1xP1) == true
     @test integrate(cohomology_class(anticanonical_divisor(X1_P1xP1))^dim(X1_P1xP1)) == 44
-    @test rank(picard_group(X2_P1xP1)) == 3
+    @test torsion_free_rank(picard_group(X2_P1xP1)) == 3
     @test is_fano(X2_P1xP1) == true
     @test integrate(cohomology_class(anticanonical_divisor(X2_P1xP1))^dim(X2_P1xP1)) == 48
-    @test rank(picard_group(X3_P1xP1)) == 3
+    @test torsion_free_rank(picard_group(X3_P1xP1)) == 3
     @test is_fano(X3_P1xP1) == true
     @test integrate(cohomology_class(anticanonical_divisor(X3_P1xP1))^dim(X3_P1xP1)) == 52
   end
diff --git a/test/AlgebraicGeometry/ToricVarieties/toric_blowdowns.jl b/test/AlgebraicGeometry/ToricVarieties/toric_blowdowns.jl
index 0b56eaf9aeb1..153a8b40f01b 100644
--- a/test/AlgebraicGeometry/ToricVarieties/toric_blowdowns.jl
+++ b/test/AlgebraicGeometry/ToricVarieties/toric_blowdowns.jl
@@ -4,8 +4,8 @@
   bl = blow_up(P2, [1, 1])
 
   @testset "Basic tests for simple toric blowdown" begin
-    @test rank(domain(grid_morphism(bl))) == 2
-    @test rank(codomain(grid_morphism(bl))) == 2
+    @test torsion_free_rank(domain(grid_morphism(bl))) == 2
+    @test torsion_free_rank(codomain(grid_morphism(bl))) == 2
     @test matrix(morphism_on_torusinvariant_weil_divisor_group(bl)) == matrix(ZZ, [1 0 0; 0 1 0; 0 0 1; 1 1 0])
     @test matrix(morphism_on_torusinvariant_cartier_divisor_group(bl)) == matrix(morphism_on_torusinvariant_weil_divisor_group(bl))
   end
diff --git a/test/AlgebraicGeometry/ToricVarieties/toric_blowups.jl b/test/AlgebraicGeometry/ToricVarieties/toric_blowups.jl
index ca44960d0e88..b35169a82818 100644
--- a/test/AlgebraicGeometry/ToricVarieties/toric_blowups.jl
+++ b/test/AlgebraicGeometry/ToricVarieties/toric_blowups.jl
@@ -22,7 +22,7 @@
     @test betti_number(BP2, 3) == 0
     @test betti_number(BP2, 4) == 1
     @test euler_characteristic(BP2) == 4
-    @test rank(picard_group(BP2)) == 2
+    @test torsion_free_rank(picard_group(BP2)) == 2
   end
 
   @testset "Trigger issue of PR3006" begin
diff --git a/test/AlgebraicGeometry/ToricVarieties/toric_divisor_classes.jl b/test/AlgebraicGeometry/ToricVarieties/toric_divisor_classes.jl
index 8a185f7694bf..b72bc1c8d04e 100644
--- a/test/AlgebraicGeometry/ToricVarieties/toric_divisor_classes.jl
+++ b/test/AlgebraicGeometry/ToricVarieties/toric_divisor_classes.jl
@@ -20,7 +20,7 @@
   end
   
   @testset "Basic attributes" begin
-    @test rank(parent(divisor_class(DC2))) == 2
+    @test torsion_free_rank(parent(divisor_class(DC2))) == 2
     @test dim(toric_variety(DC2)) == 2
   end
   
diff --git a/test/AlgebraicGeometry/ToricVarieties/total_space.jl b/test/AlgebraicGeometry/ToricVarieties/total_space.jl
index 50bb4be053a9..0e8c110e8a10 100644
--- a/test/AlgebraicGeometry/ToricVarieties/total_space.jl
+++ b/test/AlgebraicGeometry/ToricVarieties/total_space.jl
@@ -9,7 +9,7 @@
       @test is_smooth(X) == true
       @test !is_fano(X)
       @test !is_complete(X)
-      @test rank(picard_group(X)) == 1
+      @test torsion_free_rank(picard_group(X)) == 1
       @test dim(X) == 3
       @test (degree(canonical_bundle(X)) == 0) == (a - b == -2)
     end
@@ -23,7 +23,7 @@
         @test is_smooth(X) == true
         @test !is_fano(X)
         @test !is_complete(X)
-        @test rank(picard_group(X)) == rank(picard_group(S))
+        @test torsion_free_rank(picard_group(X)) == torsion_free_rank(picard_group(S))
         @test dim(X) == 3
         @test degree(canonical_bundle(X)) == 0
       end
@@ -35,7 +35,7 @@
         X = total_space(canonical_divisor(S))
         @test is_smooth(X) == true
         @test !is_fano(X)
-        @test rank(picard_group(X)) == rank(picard_group(S))
+        @test torsion_free_rank(picard_group(X)) == torsion_free_rank(picard_group(S))
         @test dim(X) == 3
         @test degree(canonical_bundle(X)) == 0
       end
diff --git a/test/Combinatorics/SimplicialComplexes.jl b/test/Combinatorics/SimplicialComplexes.jl
index fbbb8e463632..611809b746a0 100644
--- a/test/Combinatorics/SimplicialComplexes.jl
+++ b/test/Combinatorics/SimplicialComplexes.jl
@@ -55,9 +55,9 @@
     @test !is_trivial(H0)
     @test !is_trivial(H1)
     @test !is_trivial(H2)
-    @test rank(H0) == 1
-    @test rank(H1) == 2
-    @test rank(H2) == 1
+    @test torsion_free_rank(H0) == 1
+    @test torsion_free_rank(H1) == 2
+    @test torsion_free_rank(H2) == 1
   end
 
   @testset "is_isomorphic" begin
diff --git a/test/Rings/hilbert.jl b/test/Rings/hilbert.jl
index 88d2a11c2e42..01a4c82ca5b5 100644
--- a/test/Rings/hilbert.jl
+++ b/test/Rings/hilbert.jl
@@ -104,13 +104,13 @@ end
   JJ = ideal(RR, X^2 - Y^6);
   A, _ = quo(base_ring(JJ), JJ);
   (numer1, denom1), (H, iso) = multi_hilbert_series(A);
-  @test is_free(H) && isone(rank(H))
+  @test is_free(H) && isone(torsion_free_rank(H))
   S, t = laurent_polynomial_ring(ZZ, "t");
   (numer2, denom2), (H, iso) = multi_hilbert_series(A; parent=S);
-  @test is_free(H) && isone(rank(H))
+  @test is_free(H) && isone(torsion_free_rank(H))
   Smult, (T,) = polynomial_ring(ZZ, ["t"]);
   (numer3, denom3), (H, iso) = multi_hilbert_series(A; parent=Smult);
-  @test is_free(H) && isone(rank(H))
+  @test is_free(H) && isone(torsion_free_rank(H))
   @test numer1 == evaluate(numer2, T)
   @test numer3 == evaluate(numer2, first(gens(parent(numer3))))
 end