Gillespie posed two questions in [Front. Math. China 12 (2017) 97-115], one of which states
that “for what rings R do we have K (AC)= K (R-Inj)?”. We give an answer to such a question …

Throughout R is an associative ring with identity and all modules are unitary. Unless stated
otherwise, an R-module will be understood to be a left R-module. As usual, pdR (M) and idR …

The study of rings and modules with homological criteria is a cornerstone of commutative
algebra. Let $ R $ be a commutative Noetherian ring with identity (not necessarily local) and …

By generalizing a recent result of Rickard about relations between unbounded derived
categories and finitistic dimension, we obtain several new characterizations of noetherian …

Let $\varphi\colon R\rightarrow A $ be a ring homomorphism, where $ R $ is a commutative
noetherian ring and $ A $ is a finite $ R $-algebra. We give criteria for detecting the ascent …

In 1966, Auslander introduced the notion of the $ G $-dimension of a finitely generated
module over a Cohen-Macaulay noetherian ring and found the basic properties of these …

One of the open problems in Gorenstein homological algebra is: when is the class of
Gorenstein injective modules closed under arbitrary direct limits? It is known that if the class …

We prove that the class of Gorenstein injective modules is covering if and only if it is closed
under direct limits. This adds to the list of examples that support Enochs conjecture: Every …

Let R be a general ring. Duality pairs of R-modules were introduced by Holm-Jørgensen.
Most examples satisfy further properties making them what we call semi-complete duality …

In this paper we mainly study the properties of dual modules over k-Gorenstein rings. For a k-
Gorenstein ring Λ we show that the right self-injective dimension is less than or equal to k if …