A concrete description of all graded maximal Cohen–Macaulay modules of rank one and two over the non-isolated singularities of type y3 1 +y 2 1y3−y 2y3 is given. For this purpose we construct an alghoritm that provides extensions of MCM modules over an arbitrary hypersurface.

We study reflexive modules over one dimensional Cohen-Macaulay rings. Our key technique exploits the concept of I I -Ulrich modules.

This paper introduces a new notion of depth for complexes; it agrees with the classical definition for modules, and coincides with earlier extensions to complexes, whenever those are defined. Techniques are developed leading to a quick proof of an extension of the Improved New Intersection Theorem (this uses Hochster’s big Cohen-Macaulay modules), and also a generalization of the “depth formula...

We present various approaches to J. Herzog's theory of generalized local cohomology and explore its main aspects, e.g., (non-)vanishing results as well a general duality theorem which extends, much broader class rings, previous by Herzog-Zamani Suzuki. As an application, we establish prescribed upper bound for the projective dimension module satisfying suitable cohomological conditions, derive ...

Abstract We consider the dominant dimension of an order over a Cohen-Macaulay ring in category centrally modules. There is canonical tilting module case positive and we give upper bound on global its endomorphism ring.

Let (R,m) be a local Cohen-Macaulay ring whose m-adic completion R̂ has an isolated singularity. We verify the following conjecture of F.-O. Schreyer: R has finite Cohen-Macaulay type if and only if R̂ has finite Cohen-Macaulay type. We show also that the hypersurface k[[x0, . . . , xd]]/(f) has finite Cohen-Macaulay type if and only if k [[x0, . . . , xd]]/(f) has finite Cohen-Macaulay type, whe...

For finitely generated module M over a local ring R, the conventional notions of complete intersection dimension CI-dimRM and CohenMacaulay dimension CM-dimRM do not extend to cover the case of infinitely generated modules. In this paper we introduce similar invariants for not necessarily finitely generated modules, (namely, complete intersection flat and Cohen-Macaulay flat dimensions) which f...

in this paper, we introduce a subclass of chordal graphs which contains $d$-trees and show that their complement are vertex decomposable and so is shellable and sequentially cohen-macaulay.

We introduce the notion of residual intersections modules and prove their existence. show that projective dimension one have Cohen-Macaulay intersections, namely they satisfy relevant Artin-Nagata property. then establish a formula for core orientable satisfying certain homological conditions, extending previous results Corso, Polini, Ulrich on modules. Finally, we provide examples classes our ...