It is well known that, given a ring R, if M is an R-module such that pdR (M)<∞, then GidR
(M)= idR (M)(Holm, 2004). This shows in particular that if R is a Noetherian ring such that …

We study the Gorenstein weak global dimension of associative rings and its relation to the
Gorenstein global dimension. In particular, we prove the conjecture that the Gorenstein …

In basic homological algebra, the projective, injective and flat dimensions of modules play
an important and fundamental role. In this paper, the closely related Gorenstein projective …

In this article we investigate the relations between the Gorenstein projective dimensions of Λ-
modules and their socles for n-minimal Auslander–Gorenstein algebras Λ. First we give a …

We expand on two existing characterizations of rings of Gorenstein (weak) global dimension
zero and give two new characterizations of rings of finite Gorenstein (weak) global …

ABSTRACT Let R⊂ A be a Frobenius extension of rings. We prove that:(1) for any left A-
module M, AM is Gorenstein projective (injective) if and only if the underlying left R-module …

In this paper, we extend the well-known Hilbert's syzygy theorem to the Gorenstein
homological dimensions of rings. Also, we study the Gorenstein homological dimensions of …

Following our previous work about quasi-projective dimension [11], in this paper, we
introduce quasi-injective dimension as a generalization of injective dimension. We recover …

Let $ R $ be a Ding-Chen ring. Yang\cite {Yang2012} and Zhang\cite {Zhang2015} asked
whether or not every $ R $-module has finite Ding projective or Ding injective dimension. In …

Let $ R $ be any ring. We prove that all direct products of flat right $ R $-modules have finite
flat dimension if and only if each finitely generated left ideal of $ R $ has finite projective …