We answer a question of Celikbas, Dao, and Takahashi by establishing the following
characterization of Gorenstein rings: a commutative noetherian local ring (R,\mathfrak m)(R …

A left and right Noetherian ringRis called Gorenstein if bothRRandRRhave finite injective
dimensions. These rings were studied by Bass for the commutative case and Iwanaga for …

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 …

The main purpose of this article is to present some applications of the notion of Gorenstein
injective dimension of complexes over an associative ring. Among the applications, we give …

In this article, we investigate the Gorenstein global dimension with respect to the
recollements of abelian categories. With the invariants spli and silp of the categories, we …

In this paper, we study the relative homological dimension based on the class of projectively
coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and …

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 …

Let 𝒜 be an abelian category. In this paper, we investigate the global (𝒳, 𝒴)-Gorenstein
projective dimension gl. GPD (𝒳, 𝒴)(𝒜), associated to a GP-admissible pair (𝒳, 𝒴). We give …

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 …

In this paper we develop the homological properties of the Gorenstein $(\Le,\A) $-flat $ R $-
modules $\GF_ {(\Flat (R),\A)} $ proposed by Gillespie,\linebreak where the class …