We show that if M is a finitely generated module over a commutative Noetherian local ring R
and I is a dimension one ideal of R (ie, dim RI= 1), then the local cohomology modules HIi …

Let R be a commutative Noetherian ring. It is shown that the finitely generated R-module M
with finite Gorenstein dimension is reflexive if and only if M p is reflexive for p∈ Spec (R) …

The main result asserts that a local commutative Noetherian ring is Gorenstein, if it
possesses a non-zero cyclic module of finite Gorenstein injective dimension. From this …

Let R be a commutative Noetherian ring, I and J be two ideals of R and M be an R-module
(not necessary I-torsion). In this paper among other things, it is shown that if dim M≤ 1, then …

Let A be a commutative ring, and let I be an ideal of A. The cohomological dimension ofl in
A, denoted by cd (A, I), is the smallest integer n such that the local cohomology modules …

Let R be a commutative Noetherian ring. Let a and b be ideals of R and let N be a finitely
generated R-module. We introduce a generalization of the b-finiteness dimension of fb a (N) …

COFINITENESS OF LOCAL COHOMOLOGY MODULES FOR IDEALS OF DIMENSION ONE
Page 1 K.-I. Yoshida Nagoya Math. J. Vol. 147 (1997), 179-191 COFINITENESS OF LOCAL …

Let $(R,\mathfrak {m}) $ be a Gorenstein local ring of dimension $ d> 0$ and let $ I $ be an
ideal of $ R $ such that $(0)\ne I\subsetneq R $ and $ R/I $ is a Cohen-Macaulay ring of …

We answer a question of Celikbas, Dao, and Takahashi by establishing the following
characterization of Gorenstein rings: a commutative noetherian local ring (R,\mathfrak m)(R …

Let $(R,\m) $ be a Noetherian local ring. Consider the notion of homological dimension of a
module, denoted H-dim, for H= Reg, CI, CI $ _* $, G, G $^* $ or CM. We prove that, if for a …