Asymptotic depth of Ext modules over complete intersection rings

Associated Graphs of Modules Over Commutative Rings

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper we introduce a new graph associated to modules over commutative rings. We study the relationship between the algebraic properties of modules and their associated graphs. A topological characterization for the completeness of the special subgraphs is presented. Also modules whose associated graph is complete...

The Cohomology of Modules over a Complete Intersection Ring

We investigate the cohomology of modules over commutative complete intersection rings. The first main result is that if M is an arbitrary module over a complete intersection ring R, and if Ext 2n R (M, M) = 0 for some n ≥ 1 then M has finite projective dimension. The second main result gives a new proof of the fact that the support variety of a Cohen-Macaulay module whose completion is indecomp...

On a Depth Formula for Modules over Local Rings

We prove that for modules M and N over a local ring R, the depth formula: depthR M + depthR N − depthR = depthR Tor R s (M,N) − s, where s = sup{i | Tor i (M,N) 6= 0}, holds under certain conditions. This adds to the list cases where the depth formula, which extends the classical Auslander-Buchsbaum equality, is satisfied.

A Classification of Modules over Complete Discrete Valuation Rings

NONNIL-NOETHERIAN MODULES OVER COMMUTATIVE RINGS

In this paper we introduce a new class of modules which is closely related to the class of Noetherian modules. Let $R$ be a commutative ring with identity and let $M$ be an $R$-module such that $Nil(M)$ is a divided prime submodule of $M$. $M$ is called a Nonnil-Noetherian $R$-module if every nonnil submodule of $M$ is finitely generated. We prove that many of the properties of Noetherian modul...