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 …

In the original paper on Gorenstein rings, Bass [1] characterizes Gorenstein rings as those
commutative Noetherian local rings A which are Cohen-Macaulay and satisfy nn {A)= 1 …

Throughout this paper, the word" ring" will mean" commutative,(associative,) Noetherian ring
with a non-zero multiplicative identity". In [9], I discussed the Cousin Complex, C (M), for a …

Inspired in one of Auslander's characterizations of Gorenstein projective modules in [I],
Enochs and Jenda in [5] define t, he left derived functors of Horn (instead of the usual right …

The main result asserts that a local commutative Noetherian ring is Gorenstein, if it
possesses a non-zero cyclic module of finite Gorenstein injective dimension. From this …

In this paper, we study certain properties of modules of finite Gorenstein projective, injective
and flat dimensions. We examine conditions which imply that all Gorenstein projective …

The starting point for the discussion in the present paper is another result of Levin and
Vasconcelos. In [13], Theorem 2.2, they proved that, if R is a Gorenstein local ring, then a fg …

In case A has finite Krull-dimension, say d, it is well-known by Bass [2] that A is a Gorenstein
ring if and only if ExtiA (M, A)=(0) for every finitely generated A-module M and for every …

Let M be a finitely generated module over a commutative noetherian ring A (with 1). Then M
is called qtcusi-perfect if G-dim M= gradeM. Perfect modules (ie projective dimension …

The object of this article is to determine when a commutative Artin local ring A is the
homomorphic image ofa Gorenstein ring t F in such a way that the kernel of the …