Add is_finitely_generated for FPModules and fix is_noetherian

src/Module.jl

@@ -26,6 +26,27 @@ function check_parent(M::FPModule{T}, N::FPModule{T}) where T <: RingElement
 end
 
 is_finite(M::FPModule{<:FinFieldElem}) = true
+is_finitely_generated(M::FPModule) = true
+is_finitely_generated(M::Module) = isfinite(ngens(M)) || throw(NotImplementedError(:is_finitely_generated, M))
+
+@doc raw"""
+    is_noetherian(M::Module)
+
+Check if the module $M$ is Noetherian. This is currently implemented only for finitely generated modules
+in which case it is sufficient to check whether the base ring is Noetherian.
+
+# Examples
+```jldoctest
+julia> R, x = polynomial_ring(ZZ, [:x]);
+
+julia> M = free_module(R, 2)
+Free module of rank 2 over R
+
+julia> is_noetherian(M)
+true
+```
+"""
+is_noetherian(M::Module) = (is_noetherian(base_ring(M)) && is_finitely_generated(M)) || throw(NotImplementedError(:is_noetherian, M))
 
 function is_sub_with_data(M::FPModule{T}, N::FPModule{T}) where T <: RingElement
   fl = is_submodule(N, M)

src/Rings.jl

@@ -265,7 +265,6 @@ is_noetherian(::Integers) = true
 is_noetherian(R::Union{PolyRing, MPolyRing, LaurentPolyRing, LaurentMPolyRing}) = is_noetherian(coefficient_ring(R))
 is_noetherian(R::Union{MSeriesRing, SeriesRing}) = is_noetherian(base_ring(R))
 is_noetherian(R::ResidueRing) = is_noetherian(base_ring(R)) || throw(NotImplementedError(:is_noetherian, R))
-is_noetherian(M::Module) = is_noetherian(base_ring(M)) || throw(NotImplementedError(:is_noetherian, M))
 
 @doc raw"""
     krull_dim(R::Ring)

src/exports.jl

@@ -301,6 +301,7 @@ export is_even
 export is_exact_type
 export is_finite
 export is_finite_order
+export is_finitely_generated
 export is_free
 export is_gen
 export is_hermitian