diff --git a/src/FunField/HessQR.jl b/src/FunField/HessQR.jl
index b5a0d86eca..b5d7d6e3ba 100644
--- a/src/FunField/HessQR.jl
+++ b/src/FunField/HessQR.jl
@@ -111,6 +111,8 @@ function expressify(a::HessQRElem; context = nothing)
                               expressify(a.g, context = context)))
 end
 
+Hecke.characteristic(::HessQR) = 0
+
 function Hecke.integral_split(a::Generic.RationalFunctionFieldElem{QQFieldElem}, S::HessQR)
   if iszero(a)
     return zero(S), one(S)
diff --git a/src/Misc/nmod_poly.jl b/src/Misc/nmod_poly.jl
index 510d979da6..5e3d9ad6e2 100644
--- a/src/Misc/nmod_poly.jl
+++ b/src/Misc/nmod_poly.jl
@@ -199,6 +199,9 @@ function resultant_ideal_pp(f::PolyRingElem{T}, g::PolyRingElem{T}) where T <: R
       s = gcd(lift(res), pn)
       if !isone(s)
         new_pn = divexact(pn, s)
+        if is_one(new_pn)
+          return zero(R)
+        end
         R1 = residue_ring(ZZ, S(new_pn), cached = false)[1]
         R1t = polynomial_ring(R1, "y", cached = false)[1]
         f2 = R1t(T[R1(lift(coeff(f, i))) for i = 0:degree(f)])
diff --git a/src/NumFieldOrd/NfOrd/Ideal/Ideal.jl b/src/NumFieldOrd/NfOrd/Ideal/Ideal.jl
index 2399da4d0d..66cf12b241 100644
--- a/src/NumFieldOrd/NfOrd/Ideal/Ideal.jl
+++ b/src/NumFieldOrd/NfOrd/Ideal/Ideal.jl
@@ -1033,6 +1033,9 @@ function _minmod(a::ZZRingElem, b::AbsNumFieldOrderElem)
 end
 
 function _minmod_easy(a::ZZRingElem, b::AbsSimpleNumFieldOrderElem)
+  if is_one(a)
+    return a
+  end
   Zk = parent(b)
   k = number_field(Zk)
   if fits(Int, a)
@@ -1053,6 +1056,9 @@ function _minmod_easy(a::ZZRingElem, b::AbsSimpleNumFieldOrderElem)
 end
 
 function _minmod_easy_pp(a::ZZRingElem, b::AbsSimpleNumFieldOrderElem)
+  if isone(a)
+    return one(a)
+  end
   Zk = parent(b)
   k = number_field(Zk)
   if fits(Int, a)
@@ -1147,7 +1153,6 @@ end
 
 
 function _minmod_comp(a::ZZRingElem, b::AbsSimpleNumFieldOrderElem)
-
   Zk = parent(b)
   k = number_field(Zk)
   acom, auncom = ppio(a, index(Zk))