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 …

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 …

The Chouinard formula for the injective dimension of a module over a noetherian ring is
extended to Gorenstein injective dimension. Specifically, if $ M $ is a module of finite …

We study the relative Gorenstein projective global dimension of a ring with respect to a
weakly Wakamatsu tilting module C. We prove that this relative global dimension is finite if …

If M is a nonzero finitely generated module over a commutative Noetherian local ring R such
that M has finite injective dimension and finite Gorenstein dimension, then it follows from a …

We obtain various characterizations of commutative Noetherian local rings (R, m) in terms of
homological dimensions of certain finitely generated modules. Our argument has a series of …

In this paper, we study Gorenstein projective and flat modules over a Noetherian ring R. For
an R-module M, we show that Gorenstein projective dimension of M is finite if and only if …

Let R be a commutative Noetherian ring and let M be a finite (that is, finitely generated) R-
module. The notion grade of M, grade M, has been introduced by Rees as the least integer …

Let R be a ring with an identity and, for a left Λ-module RM, pd (M) and ίd (M) denote the
projective and injective dimension of RM, respectively. A (left and right) noether ring R is …

Let R be a ring. A left R-module M is called GI-injective if for any Gorenstein injective left R-
module N. It is shown that a left R-module M over any ring R is GI-injective if and only if M is …