diff --git a/Project.toml b/Project.toml
index 23c03e103c..2c63e04f09 100644
--- a/Project.toml
+++ b/Project.toml
@@ -13,7 +13,7 @@ SHA = "ea8e919c-243c-51af-8825-aaa63cd721ce"
 TOML = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
 
 [compat]
-AbstractAlgebra = "0.44.1"
+AbstractAlgebra = "0.44.2"
 FLINT_jll = "^300.100.100"
 Libdl = "1.6"
 LinearAlgebra = "1.6"
diff --git a/src/Exports.jl b/src/Exports.jl
index cb77d506d3..ee29b244b5 100644
--- a/src/Exports.jl
+++ b/src/Exports.jl
@@ -351,7 +351,6 @@ export is_less_real
 export is_less_root_order
 export is_lower_triangular
 export is_negative
-export is_nilpotent
 export is_nonnegative
 export is_nonpositive
 export is_nonzero
diff --git a/src/HeckeMoreStuff.jl b/src/HeckeMoreStuff.jl
index 7abe92c401..262ab8148c 100644
--- a/src/HeckeMoreStuff.jl
+++ b/src/HeckeMoreStuff.jl
@@ -346,38 +346,6 @@ function gcdx(a::ResElem{T}, b::ResElem{T}) where {T<:IntegerUnion}
   return R(G), R(U) * R(u), R(U) * R(v)
 end
 
-@doc raw"""
-    is_unit(f::Union{ZZModPolyRingElem,zzModPolyRingElem}) -> Bool
-
-Tests if $f$ is a unit in the polynomial ring, i.e. if
-$f = u + n$ where $u$ is a unit in the coeff. ring
-and $n$ is nilpotent.
-"""
-function is_unit(f::T) where {T<:Union{ZZModPolyRingElem,zzModPolyRingElem}}
-  if !is_unit(constant_coefficient(f))
-    return false
-  end
-  for i = 1:degree(f)
-    if !is_nilpotent(coeff(f, i))
-      return false
-    end
-  end
-  return true
-end
-
-@doc raw"""
-    is_nilpotent(a::ResElem{ZZRingElem}) -> Bool
-    is_nilpotent(a::ResElem{Integer}) -> Bool
-
-Tests if $a$ is nilpotent.
-"""
-function is_nilpotent(a::ResElem{T}) where {T<:IntegerUnion}
-  #a is nilpontent if it is divisible by all primes divising the modulus
-  # the largest exponent a prime can divide is nbits(m)
-  l = nbits(modulus(a))
-  return iszero(a^l)
-end
-
 function inv(f::T) where {T<:Union{ZZModPolyRingElem,zzModPolyRingElem}}
   if !is_unit(f)
     error("impossible inverse")
diff --git a/src/antic/nf_elem.jl b/src/antic/nf_elem.jl
index 312f88efff..71be6296f1 100644
--- a/src/antic/nf_elem.jl
+++ b/src/antic/nf_elem.jl
@@ -130,14 +130,6 @@ function iszero(a::AbsSimpleNumFieldElem)
   return @ccall libflint.nf_elem_is_zero(a::Ref{AbsSimpleNumFieldElem}, a.parent::Ref{AbsSimpleNumField})::Bool
 end
 
-@doc raw"""
-    is_unit(a::AbsSimpleNumFieldElem)
-
-Return `true` if the given number field element is invertible, i.e. nonzero,
-otherwise return `false`. Note, this does not take the maximal order into account.
-"""
-is_unit(a::AbsSimpleNumFieldElem) = !iszero(a)
-
 @doc raw"""
     isinteger(a::AbsSimpleNumFieldElem)
 
diff --git a/src/arb/Complex.jl b/src/arb/Complex.jl
index 0e36d14904..e32895f99c 100644
--- a/src/arb/Complex.jl
+++ b/src/arb/Complex.jl
@@ -447,10 +447,6 @@ end
 #
 ################################################################################
 
-function is_unit(x::ComplexFieldElem)
-  !iszero(x)
-end
-
 @doc raw"""
     iszero(x::ComplexFieldElem)
 
diff --git a/src/arb/acb.jl b/src/arb/acb.jl
index bf7031d7a3..95b3fbc313 100644
--- a/src/arb/acb.jl
+++ b/src/arb/acb.jl
@@ -458,10 +458,6 @@ end
 #
 ################################################################################
 
-function is_unit(x::AcbFieldElem)
-  !iszero(x)
-end
-
 @doc raw"""
     iszero(x::AcbFieldElem)
 
diff --git a/src/arb/arb.jl b/src/arb/arb.jl
index f7abff284b..4a5a0c5c58 100644
--- a/src/arb/arb.jl
+++ b/src/arb/arb.jl
@@ -450,10 +450,6 @@ end
 #
 ################################################################################
 
-function is_unit(x::ArbFieldElem)
-  !iszero(x)
-end
-
 @doc raw"""
     iszero(x::ArbFieldElem)
 
diff --git a/src/flint/fmpq.jl b/src/flint/fmpq.jl
index 39bca1ca01..ae22e4d284 100644
--- a/src/flint/fmpq.jl
+++ b/src/flint/fmpq.jl
@@ -113,8 +113,6 @@ is_one(a::QQFieldElemOrPtr) = isinteger(a) && is_one(_num_ptr(a))
 
 is_zero(a::QQFieldElemOrPtr) = is_zero(_num_ptr(a))
 
-is_unit(a::QQFieldElem) = !iszero(a)
-
 isinteger(a::QQFieldElemOrPtr) = is_one(_den_ptr(a))
 
 isfinite(::QQFieldElem) = true
diff --git a/src/flint/fmpq_mpoly.jl b/src/flint/fmpq_mpoly.jl
index f4e9398ce9..cab8b11af7 100644
--- a/src/flint/fmpq_mpoly.jl
+++ b/src/flint/fmpq_mpoly.jl
@@ -104,10 +104,6 @@ function is_term(a::QQMPolyRingElem)
   return length(a) == 1
 end
 
-function is_unit(a::QQMPolyRingElem)
-  return length(a) == 1 && total_degree(a) == 0 && is_unit(coeff(a, 1))
-end
-
 function is_constant(a::QQMPolyRingElem)
   b = @ccall libflint.fmpq_mpoly_is_fmpq(a::Ref{QQMPolyRingElem}, parent(a)::Ref{QQMPolyRing})::Cint
   return Bool(b)
diff --git a/src/flint/fmpz_mod_mpoly.jl b/src/flint/fmpz_mod_mpoly.jl
index 2254152c3d..e7d44cd2e7 100644
--- a/src/flint/fmpz_mod_mpoly.jl
+++ b/src/flint/fmpz_mod_mpoly.jl
@@ -106,10 +106,6 @@ for (etype, rtype, ftype, ctype) in (
       return length(a) == 1
     end
 
-    function is_unit(a::($etype))
-      return length(a) == 1 && total_degree(a) == 0 && is_unit(coeff(a, 1))
-    end
-
     function is_constant(a::($etype))
       return Bool(@ccall libflint.fmpz_mod_mpoly_is_fmpz(a::Ref{($etype)}, parent(a)::Ref{($rtype)})::Cint)
     end
diff --git a/src/flint/fmpz_mpoly.jl b/src/flint/fmpz_mpoly.jl
index f83fb2be72..73bb15c4d1 100644
--- a/src/flint/fmpz_mpoly.jl
+++ b/src/flint/fmpz_mpoly.jl
@@ -95,10 +95,6 @@ function is_term(a::ZZMPolyRingElem)
   return length(a) == 1
 end
 
-function is_unit(a::ZZMPolyRingElem)
-  return length(a) == 1 && total_degree(a) == 0 && is_unit(coeff(a, 1))
-end
-
 function is_constant(a::ZZMPolyRingElem)
   b = @ccall libflint.fmpz_mpoly_is_fmpz(a::Ref{ZZMPolyRingElem}, parent(a)::Ref{ZZMPolyRing})::Cint
   return Bool(b)
diff --git a/src/flint/fq.jl b/src/flint/fq.jl
index ab363b9b96..ae4d2093ef 100644
--- a/src/flint/fq.jl
+++ b/src/flint/fq.jl
@@ -81,8 +81,6 @@ finite field, otherwise return `false`.
 """
 is_gen(a::FqPolyRepFieldElem) = a == gen(parent(a))
 
-is_unit(a::FqPolyRepFieldElem) = !is_zero(a)
-
 function characteristic(a::FqPolyRepField)
   d = ZZRingElem()
   @ccall libflint.__fq_ctx_prime(d::Ref{ZZRingElem}, a::Ref{FqPolyRepField})::Nothing
diff --git a/src/flint/fq_default.jl b/src/flint/fq_default.jl
index 15fa7165f2..0cf3b78bcb 100644
--- a/src/flint/fq_default.jl
+++ b/src/flint/fq_default.jl
@@ -60,8 +60,6 @@ isone(a::FqFieldElem) = @ccall libflint.fq_default_is_one(a::Ref{FqFieldElem}, a
 
 _is_gen(a::FqFieldElem) = a == _gen(parent(a))
 
-is_unit(a::FqFieldElem) = !iszero(a)
-
 function characteristic(a::FqField)
   d = ZZRingElem()
   @ccall libflint.fq_default_ctx_prime(d::Ref{ZZRingElem}, a::Ref{FqField})::Nothing
diff --git a/src/flint/fq_nmod.jl b/src/flint/fq_nmod.jl
index f10daf4a0a..1b53fbcd74 100644
--- a/src/flint/fq_nmod.jl
+++ b/src/flint/fq_nmod.jl
@@ -81,8 +81,6 @@ isone(a::fqPolyRepFieldElem) = @ccall libflint.fq_nmod_is_one(a::Ref{fqPolyRepFi
 
 is_gen(a::fqPolyRepFieldElem) = a == gen(parent(a)) # there is no is_gen in flint
 
-is_unit(a::fqPolyRepFieldElem) = @ccall libflint.fq_nmod_is_invertible(a::Ref{fqPolyRepFieldElem}, a.parent::Ref{fqPolyRepField})::Bool
-
 function characteristic(a::fqPolyRepField)
   return ZZ(a.n)
 end
diff --git a/src/flint/fq_nmod_mpoly.jl b/src/flint/fq_nmod_mpoly.jl
index 6557697a2f..d29346995a 100644
--- a/src/flint/fq_nmod_mpoly.jl
+++ b/src/flint/fq_nmod_mpoly.jl
@@ -91,10 +91,6 @@ function is_term(a::fqPolyRepMPolyRingElem)
   return length(a) == 1
 end
 
-function is_unit(a::fqPolyRepMPolyRingElem)
-  return is_constant(a)
-end
-
 function is_constant(a::fqPolyRepMPolyRingElem)
   b = @ccall libflint.fq_nmod_mpoly_is_fq_nmod(a::Ref{fqPolyRepMPolyRingElem}, parent(a)::Ref{fqPolyRepMPolyRing})::Cint
   return Bool(b)
diff --git a/src/flint/gfp_elem.jl b/src/flint/gfp_elem.jl
index 8a44ab0103..1dab8ecbaa 100644
--- a/src/flint/gfp_elem.jl
+++ b/src/flint/gfp_elem.jl
@@ -57,8 +57,6 @@ iszero(a::fpFieldElem) = a.data == 0
 
 isone(a::fpFieldElem) = a.data == 1
 
-is_unit(a::fpFieldElem) = a.data != 0
-
 modulus(R::fpField) = R.n
 
 function deepcopy_internal(a::fpFieldElem, dict::IdDict)
diff --git a/src/flint/gfp_fmpz_elem.jl b/src/flint/gfp_fmpz_elem.jl
index 7a89b1117f..dfc955d479 100644
--- a/src/flint/gfp_fmpz_elem.jl
+++ b/src/flint/gfp_fmpz_elem.jl
@@ -60,8 +60,6 @@ function one(R::FpField)
   end
 end
 
-is_unit(a::FpFieldElem) = a.data != 0
-
 modulus(R::FpField) = R.n
 
 characteristic(F::FpField) = modulus(F)
diff --git a/src/flint/nmod.jl b/src/flint/nmod.jl
index b04266f62e..f8c7442fa2 100644
--- a/src/flint/nmod.jl
+++ b/src/flint/nmod.jl
@@ -50,9 +50,7 @@ end
 
 iszero(a::zzModRingElem) = a.data == 0
 
-isone(a::zzModRingElem) = a.parent.n == 1 ? a.data == 0 : a.data == 1
-
-is_unit(a::zzModRingElem) = a.parent.n == 1 ? a.data == 0 : gcd(a.data, a.parent.n) == 1
+isone(a::zzModRingElem) = (a.parent.n == 1) || (a.data == 1)
 
 modulus(R::zzModRing) = R.n
 
diff --git a/src/flint/nmod_mpoly.jl b/src/flint/nmod_mpoly.jl
index b434177acd..ceed984e65 100644
--- a/src/flint/nmod_mpoly.jl
+++ b/src/flint/nmod_mpoly.jl
@@ -100,10 +100,6 @@ for (etype, rtype, ftype, ctype, utype) in (
       return length(a) == 1
     end
 
-    function is_unit(a::($etype))
-      return length(a) == 1 && total_degree(a) == 0 && is_unit(coeff(a, 1))
-    end
-
     function is_constant(a::($etype))
       return Bool(@ccall libflint.nmod_mpoly_is_ui(a::Ref{($etype)}, parent(a)::Ref{($rtype)})::Cint)
     end
diff --git a/src/flint/padic.jl b/src/flint/padic.jl
index 0b64f029f9..681d2d2f71 100644
--- a/src/flint/padic.jl
+++ b/src/flint/padic.jl
@@ -185,8 +185,6 @@ iszero(a::PadicFieldElem) = Bool(@ccall libflint.padic_is_zero(a::Ref{PadicField
 
 isone(a::PadicFieldElem) = Bool(@ccall libflint.padic_is_one(a::Ref{PadicFieldElem})::Cint)
 
-is_unit(a::PadicFieldElem) = !iszero(a)
-
 characteristic(R::PadicField) = 0
 
 ###############################################################################
diff --git a/src/flint/qadic.jl b/src/flint/qadic.jl
index 3d29e60f02..acf11e4002 100644
--- a/src/flint/qadic.jl
+++ b/src/flint/qadic.jl
@@ -189,8 +189,6 @@ iszero(a::QadicFieldElem) = Bool(@ccall libflint.qadic_is_zero(a::Ref{QadicField
 
 isone(a::QadicFieldElem) = Bool(@ccall libflint.qadic_is_one(a::Ref{QadicFieldElem})::Cint)
 
-is_unit(a::QadicFieldElem) = !iszero(a)
-
 characteristic(R::QadicField) = 0
 
 function shift_right(a::QadicFieldElem, n::Int)
diff --git a/src/gaussiannumbers/QQi.jl b/src/gaussiannumbers/QQi.jl
index 46e3b6543a..07ca8c1fb1 100644
--- a/src/gaussiannumbers/QQi.jl
+++ b/src/gaussiannumbers/QQi.jl
@@ -384,10 +384,6 @@ end
 #
 ###############################################################################
 
-function is_unit(a::QQiFieldElem)
-  return !iszero(a)
-end
-
 function inv!(z::QQiFieldElem, a::QQiFieldElem)
   d = abs2(a.num)
   mul!(z.num.x, a.num.x, a.den)
diff --git a/test/flint/fmpz_mod-test.jl b/test/flint/fmpz_mod-test.jl
index ff4bea8359..e1c81c8df3 100644
--- a/test/flint/fmpz_mod-test.jl
+++ b/test/flint/fmpz_mod-test.jl
@@ -89,6 +89,8 @@ end
 
   @test !is_unit(R())
   @test is_unit(R(3))
+  @test is_nilpotent(R())
+  @test !is_nilpotent(R(3))
 
   @test deepcopy(R(3)) == R(3)
 
@@ -103,6 +105,7 @@ end
   @test modulus(S) == UInt(1)
 
   @test is_unit(S())
+  @test is_nilpotent(S())
 
   @test characteristic(R) == 13
 
@@ -128,6 +131,10 @@ end
   @test_throws Exception R6(R22(1))
   @test_throws Exception R2(R3(1))
   @test_throws Exception R3(R2(1))
+
+  ZZmodZZ720,_ = residue_ring(ZZ,ZZ(720))
+  @test is_nilpotent(ZZmodZZ720(30))
+  @test count(is_nilpotent, ZZmodZZ720) == 24  # 720/(2*3*5)
 end
 
 @testset "ZZModRingElem.unary_ops" begin
diff --git a/test/flint/nmod-test.jl b/test/flint/nmod-test.jl
index c92702ba10..1759a5d266 100644
--- a/test/flint/nmod-test.jl
+++ b/test/flint/nmod-test.jl
@@ -129,6 +129,16 @@ end
   @test_throws Exception R6(R2(1))
   @test_throws Exception R2(R3(1))
   @test_throws Exception R3(R2(1))
+
+  ZZmod720,_ = residue_ring(ZZ, 720)
+  @test is_nilpotent(ZZmod720(30))
+  @test count(is_nilpotent, ZZmod720) == 24  # 720/(2*3*5)
+
+  # 64-bit overflow test:  **ASSUMES** Int is 64 bits
+  rr = 4*3^20
+  mm = 3*rr
+  R_overflow,_ = residue_ring(ZZ, mm)
+  @test is_nilpotent(R_overflow(rr))
 end
 
 @testset "zzModRingElem.unary_ops" begin