query: $\hom_R(A,B)$ is finitely generated if $R$ is noetherian
positive_passages.docid: 28518
positive_passages.text: Hom of finitely generated modules over a noetherian ring
negative_passages.docid: 49521
negative_passages.text: In an extension of finitely generated $k$-algebras the contraction of a maximal ideal is also maximal
negative_passages.docid: 63736
negative_passages.text: Every radical ideal in a Noetherian ring is a finite intersection of primes
negative_passages.docid: 143884
negative_passages.text: A non-noetherian ring with noetherian spectrum
negative_passages.docid: 12474
negative_passages.text: Does an injective endomorphism of a finitely-generated free R-module have nonzero determinant?
negative_passages.docid: 116955
negative_passages.text: Showing the existence of a certain kind of extension of a finitely generated algebra
negative_passages.docid: 140553
negative_passages.text: An ideal which is not finitely generated
negative_passages.docid: 144623
negative_passages.text: Can one avoid AC in the proof that in Noetherian rings there is a maximal element for each set?
negative_passages.docid: 46717
negative_passages.text: If $M$ is a Noetherian $R$-module, then $R/\text{Ann}(M)$ is a Noetherian ring
negative_passages.docid: 73825
negative_passages.text: Every $R$-module is a quotient of a free module
negative_passages.docid: 17304
negative_passages.text: Tensor product of two finitely-generated modules over a local ring is zero
negative_passages.docid: 121246
negative_passages.text: Projective modules and $\hom(P,\cdot)$
negative_passages.docid: 99423
negative_passages.text: Is it true every ideal of $\mathbb{Z}[x]$ is finitely generated?
negative_passages.docid: 150206
negative_passages.text: Every finitely generated algebra over a field is a Jacobson ring
negative_passages.docid: 37570
negative_passages.text: $M + N$ and $M \cap N$ are finitely generated $A$-modules implies $M$ and $N$ finitely generated using exact sequences
negative_passages.docid: 107002
negative_passages.text: Noetherian ring whose ideals have arbitrarily large number of generators
negative_passages.docid: 68202
negative_passages.text: Must an ideal generated by an irreducible element be a maximal ideal?