diff --git a/docs/src/matrix.md b/docs/src/matrix.md
index 643d8b7d50..31498dff48 100644
--- a/docs/src/matrix.md
+++ b/docs/src/matrix.md
@@ -428,7 +428,11 @@ strictly_upper_triangular_matrix(L::AbstractVector{T}) where {T <: RingElement}
 ```
 
 ```@docs
-is_upper_triangular(::MatrixElem{T}) where T <: RingElement
+is_lower_triangular(::MatrixElem)
+```
+
+```@docs
+is_upper_triangular(::MatrixElem)
 ```
 
 ```@docs
diff --git a/src/AbstractAlgebra.jl b/src/AbstractAlgebra.jl
index 085025f93c..c5de77faeb 100644
--- a/src/AbstractAlgebra.jl
+++ b/src/AbstractAlgebra.jl
@@ -37,6 +37,7 @@ import LinearAlgebra: det
 import LinearAlgebra: hessenberg
 import LinearAlgebra: ishermitian
 import LinearAlgebra: issymmetric
+import LinearAlgebra: istril
 import LinearAlgebra: istriu
 import LinearAlgebra: lu
 import LinearAlgebra: lu!
@@ -318,10 +319,11 @@ export is_trivial
 @alias is_trivial istrivial
 
 # alternative names for some functions from LinearAlgebra
-export is_hermitian, is_symmetric, is_upper_triangular
+export is_hermitian, is_symmetric, is_upper_triangular, is_lower_triangular
 
 @alias is_hermitian ishermitian
 @alias is_symmetric issymmetric
+@alias is_lower_triangular istril
 @alias is_upper_triangular istriu
 
 ###############################################################################
diff --git a/src/Matrix.jl b/src/Matrix.jl
index 7541cafb58..05a0bf8961 100644
--- a/src/Matrix.jl
+++ b/src/Matrix.jl
@@ -3350,31 +3350,24 @@ end
 ###############################################################################
 
 @doc raw"""
-    is_upper_triangular(A::MatrixElem{T}) where T <: RingElement
+    is_upper_triangular(A::MatrixElem)
 
 Return `true` if $A$ is an upper triangular matrix.
 
 Alias for `LinearAlgebra.istriu`.
 """
-function is_upper_triangular(A::MatrixElem{T}) where T <: RingElement
-   m = nrows(A)
-   n = ncols(A)
-   d = 0
-   for c = 1:n
-      for r = m:-1:1
-         if !iszero(A[r, c])
-            if r < d
-               return false
+function is_upper_triangular(M::MatrixElem)
+    m = ncols(M)
+    for i = 2:nrows(M)
+        for j = 1:min(i - 1, m)
+            if !iszero(M[i, j])
+                return false
             end
-            d = r
-            break
-         end
-      end
-   end
-   return true
+        end
+    end
+    return true
 end
 
-
 @doc raw"""
     solve_triu(U::MatElem{T}, b::MatElem{T}, unit::Bool = false) where {T <: FieldElement}
 
@@ -3420,6 +3413,30 @@ function solve_triu(U::MatElem{T}, b::MatElem{T}, unit::Bool = false) where {T <
    return X
 end
 
+###############################################################################
+#
+#
+#
+###############################################################################
+
+@doc raw"""
+    is_lower_triangular(A::MatrixElem)
+
+Return `true` if $A$ is an lower triangular matrix.
+
+Alias for `LinearAlgebra.istril`.
+"""
+function is_lower_triangular(M::MatrixElem)
+    for i = 1:nrows(M)
+        for j = i+1:ncols(M)
+            if !iszero(M[i, j])
+                return false
+            end
+        end
+    end
+    return true
+end
+
 ###############################################################################
 #
 #   Can solve
diff --git a/src/NemoStuff.jl b/src/NemoStuff.jl
index 3d6407384a..9cee15ac19 100644
--- a/src/NemoStuff.jl
+++ b/src/NemoStuff.jl
@@ -727,18 +727,6 @@ Random.gentype(::Type{T}) where {T<:FinField} = elem_type(T)
 import LinearAlgebra
 LinearAlgebra.dot(a::NCRingElem, b::NCRingElem) = a * b
 
-function is_upper_triangular(M::MatElem)
-    n = nrows(M)
-    for i = 2:n
-        for j = 1:min(i - 1, ncols(M))
-            if !iszero(M[i, j])
-                return false
-            end
-        end
-    end
-    return true
-end
-
 transpose!(A::MatrixElem) = transpose(A)
 
 function Base.div(f::PolyRingElem, g::PolyRingElem)
diff --git a/test/AbstractAlgebra-test.jl b/test/AbstractAlgebra-test.jl
index 09e3d0d8d7..f6ad5ff957 100644
--- a/test/AbstractAlgebra-test.jl
+++ b/test/AbstractAlgebra-test.jl
@@ -10,6 +10,7 @@ include("NCRings-test.jl")
 include("Rings-test.jl")
 include("Fields-test.jl")
 include("Ideals-test.jl")
+include("Matrix-test.jl")
 include("Modules-test.jl")
 include("Maps-test.jl")
 include("Benchmark-test.jl")
diff --git a/test/Matrix-test.jl b/test/Matrix-test.jl
new file mode 100644
index 0000000000..e5e6b131e9
--- /dev/null
+++ b/test/Matrix-test.jl
@@ -0,0 +1,35 @@
+@testset "Matrix.is_lower_triangular" begin
+    A = [ 1 0 0 ; 0 0 1 ; 1 0 1 ]
+    @test !is_lower_triangular(A)
+    @test !is_lower_triangular(matrix(ZZ, A))
+
+    A = [ 1 0 0 ; 0 0 1 ; 0 0 1 ]
+    @test !is_lower_triangular(A)
+    @test !is_lower_triangular(matrix(ZZ, A))
+
+    A = [ 1 0 0 ; 0 0 1 ]
+    @test !is_lower_triangular(A)
+    @test !is_lower_triangular(matrix(ZZ, A))
+
+    A = [ 1 0 0 ; 0 1 0 ]
+    @test is_lower_triangular(A)
+    @test is_lower_triangular(matrix(ZZ, A))
+end
+
+@testset "Matrix.is_upper_triangular" begin
+    A = [ 1 0 0 ; 0 0 1 ; 1 0 1 ]
+    @test !is_upper_triangular(A)
+    @test !is_upper_triangular(matrix(ZZ, A))
+
+    A = [ 1 0 0 ; 0 0 1 ; 0 0 1 ]
+    @test is_upper_triangular(A)
+    @test is_upper_triangular(matrix(ZZ, A))
+
+    A = [ 1 0 0 ; 0 0 1 ]
+    @test is_upper_triangular(A)
+    @test is_upper_triangular(matrix(ZZ, A))
+
+    A = [ 1 0 0 ; 0 1 0 ]
+    @test is_upper_triangular(A)
+    @test is_upper_triangular(matrix(ZZ, A))
+end