We give counterexamples to the following conjecture of Auslander: given a finitely
generated module M over an Artin algebra Λ, there exists a positive integer nM such that for …

Introduction. The aim of this paper is to show the relevance of a class of commutative
noetherian rings to the study of reflexive modules. They include integrally closed domains …

We show that an iteration of the procedure used to define the Gorenstein projective modules
over a commutative ring R yields exactly the Gorenstein projective modules. Specifically …

Absolutely clean and level R-modules were introduced in and used to show how Gorenstein
homological algebra can be extended to an arbitrary ring R. This led to the notion of …

The concept of Gorenstein dimension, defined by Auslander and Bridger for finitely
generated modules over a Noetherian ring, is studied in the context of finitely presented …

Let R be a commutative ring. An R-module M is said to be super finitely presented if there is
an exact sequence of R-modules where each P i is finitely generated projective. In this …

Let R be a commutative noetherian local ring and consider the set of isomorphism classes of
indecomposable totally reflexive R-modules. We prove that if this set is finite, then either it …

We introduce the notion of totally reflexive extension of rings. It unifies Gorenstein orders
and Frobenius extensions. We prove that for a totally reflexive extension, a module over the …

In this paper, we show the existence of copure injective preenvelopes over noetherian rings
and copure flat preenvelopes over commutative artinian rings. We use this to characterize …

In this paper we are going to develop a theory of Gorensteinness in graded rings associated
to certain filtrations of ideals in Gorenstein local rings. Let A be a Cohen–Macaulay local ring …