In this article, we prove the following generalization of a result of Hartshorne: Let (S, n) be a
regular local ring of dimension 4. Assume that x, y, u, v is a regular system of parameters for …

Let R be a commutative Noetherian ring and aa proper ideal of R. We show that if n:=
gradeR a, then EndR (Hn a (R))∼= Extn R (Hn a (R), R). We also prove that, for a …

Suppose (R, m) and (S, n) are commutative Noetherian local rings and ϕ: R→ S is a flat
local homomorphism with the property that the induced homomorphism R/m→ S/mS is …

Let R denote a commutative Noetherian (not necessarily local) ring, 𝔞 an ideal of R and M a
finitely generated R-module. The purpose of this article is to show that for any finitely …

Let $ R $ be a commutative Noetherian ring with non-zero identity, $\mathfrak {a} $ and
$\mathfrak {b} $ ideals of $ R $ with $\mathfrak {a}\subseteq\mathfrak {b} $, and $ M $ a …

In this paper we consider the asymptotic behavior of the ranks of the free modules in
resolutions of finitely generated modules, M, over a commutative noetherian ring, R. We …

Let R be a commutative Noetherian ring, a an ideal of R, and let M be a finitely generated R-
module. For a non-negative integer t, we prove that H_ a^ t (M) is a-cofinite whenever H_ a …

This is the first of a series of four papers describing the finitely generated modules over all
commutative noetherian rings that do not have wild representation type (with a possible …

It is well known that for a Noetherian ring R, an ideal I of R, and M a finitely generated R-
module, the local cohomology modules HiI (M) are not always finitely generated. On the …

Let R be a Noetherian ring and I, J two ideals of R. Let M be a ZD-module such that Hom R
(R/I, M/L) is finitely generated for any submodule L of M. It is shown that if t is an integer such …