Over any associative ring $ R $ it is standard to derive $\mathrm {Hom} _R (-,-) $ using
projective resolutions in the first variable, or injective resolutions in the second variable, and …

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 …

Before his death, Auslander announced that every finitely generated module over a local
Gorenstein ring has a minimal Cohen–Macaulay approximation. Yoshimo extended …

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 …

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 1966, Auslander introduced the notion of the $ G $-dimension of a finitely generated
module over a Cohen-Macaulay noetherian ring and found the basic properties of these …

Let I be an m-primary ideal of a Noetherian local ring (R, m). We consider the Gorenstein
and complete intersection properties of the associated graded ring G (I) and the fiber cone F …

Auslander and Buchweitz showed that over certain rings all finitely generated modules have
Gorenstein projective precovers (over Cohen-Macauley rings these are their maximal …

We propose a concept of module liaison that extends Gorenstein liaison of ideals and
provides an equivalence relation among unmixed modules over a commutative Gorenstein …

Factoring Out the Socle of a Gorenstein Ring 74 Page 1 j9URNAL OF ALGEBRA 55, 74-83 (1978)
Factoring Out the Socle of a Gorenstein Ring GERS~N I,. LEVIN* AND LUCHEZAR L …