Leila Khatami

ASSOCIATED PRIMES OF GENERALIZED LOCAL COHOMOLOGY MODULES

ABSTRACT We show that the first non-finitely generated generalized local cohomology modules of a finite modules M and N over a Noetherian ring R with respect to an ideal of R has only finitely many associated primes. This generalizes the corresponding result which is shown in [1] for standard local cohomology module.

Finiteness of Gorenstein injective dimension of modules

The Chouinard formula for the injective dimension of a module over a noetherian ring is extended to Gorenstein injective dimension. Specifically, if M is a module of finite positive Gorenstein injective dimension over a commutative noetherian ring R, then its Gorenstein injective dimension is the supremum of depth Rp ― width R p M p , where p runs through all prime ideals of R. It is also proved that if M is finitely generated and non-zero, then its Gorenstein injective dimension is equal to the depth of the base ring. This generalizes the classical Bass formula for injective dimension.

A Bass Formula for Gorenstein Injective Dimension

In this article a generalized version of the Bass formula is proved for finitely generated modules of finite Gorenstein injective dimension over a commutative Noetherian ring.

GRADE AND GORENSTEIN DIMENSION

Let R be a commutative Noetherian ring and let M be a finite (that is, finitely generated) R-module. The notion grade of M, grade M, has been introduced by Rees as the least integer t ≥ 0 such that Ext t R (M,R) ≠ 0, see [11]. The Gorenstein dimension of M, G-dim M, has been introduced by Auslander as the largest integer t ≥ 0 such that Ext t R (M, R) ≠ 0, see [3]. In this paper the R-module M is called G-perfect if grade M = G-dim M. It is a generalization of perfect module. We prove several results for the new concept similar to the classical results.

Gorenstein Injective and Gorenstein Flat Dimensions Under Base Change

Abstract The purpose of this paper is to investigate some connections between Gorenstein flat and Gorenstein injective dimensions of complexes over different rings.