Let R→ S be a ring homomorphism. We consider the relationships of the Gorenstein
dimensions of an R-complex X (possibly unbounded) with those of the S-complexes R Hom …

Abstract Let R⊂ S be a Frobenius extension of rings and M an S-complex. It is proven that if
the Gorenstein projective (injective) dimension of M as an S-complex is finite, then the …

For finite modules over a local ring and complexes with finitely generated homology, we
consider several homological invariants sharing some basic properties with projective …

In this article, we give a new characterization of Gorenstein projective modules. As
applications of our result, we prove that a strongly Gorenstein projective module of …

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 …

Let R be a left and right Noetherian ring and C a semidualizing R-bimodule. We introduce a
transpose Tr c M of an R-module M with respect to C which unifies the Auslander transpose …

Recently, the notion of Gorenstein AC-projective (resp., Gorenstein AC-injective) modules
was introduced in by which the so-called “Gorenstein AC-homological algebra” was …

Enochs and Jenda gave some characterizations of Gorenstein injective and projective
complexes over n-Gorenstein rings. The aim of this article is to generalize these results and …

We obtain various characterizations of commutative Noetherian local rings $(R,\fm) $ in
terms of homological dimensions of certain finitely generated modules. For example, we …

Let R be a ring and X a complex of R-modules. We investigate the relationship between the
dimensions Gppd (X) and Gpd (X) of X, where Gppd (X) is the dimension related to special …