For a left module M over a ring R, pd (M) and id (M) denote the projective and injective
dimension of M, respectively. A (left and right) noether ring R is called n-Gorenstein for an n> …

In this paper we prove that for any associative ring $ R $, and for any left $ R $-module $ M $
with finite projective dimension, the Gorenstein injective dimension $\mathrm {Gid} _R M …

Now, since Ext£+ 1 (M, K)= 0 but Ext£(M, S)= é 0 by the dual of [6, Lemma 1], Ext r (M, P)= é
0 and hence id (P)= n again by Theorem 2.(2) Decompose rR into projective …

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 …

INTRODUCTION. The main results of this paper show that homological dimensions over a
fully bounded noetherian (FBN) ring R may be computed using just simple R-modules, as …

Let R be a left and right Noetherian ring. We introduce the notion of the torsionfree
dimension of finitely generated R-modules. For any n≧0, we prove that R is a Gorenstein …

A ring for which every finitely generated right ideal is finitely presented is called a right
coherent ring. Such rings were first studied by Chase i4] as a generalization of right …

Given a homomorphism of commutative noetherian rings R→ S and an S-module N, it is
proved that the Gorenstein flat dimension of N over R, when finite, may be computed locally …

1. A local ring A of dimension n is said to be a Gorenstein ring ff Ext~(A/m, A)= 0 for i< n and
Ext~(A/m, A)~ A/m, where m is the maximal ideal of A. It can be shown (see for instance [2; p …

The global dimension gldim (R) of a Noetherian ring R, while a useful invariant when finite,
is often infinite. Several homological dimensions have been introduced to handle rings of …