Let R be a commutative Noetherian ring, 𝔞 be an ideal of R and denote the derived category
of R-modules. We investigate the theory of local homology in conjunction with Gorenstein …

On Flat and Gorenstein Flat Dimensions of Local Cohomology Modules Page 1 Canad. Math.
Bull. Vol. (), pp. – http://dx.doi.org/. /CMB---x ©Canadian Mathematical Society On Flat and …

Let R be a commutative noetherian henselian non-Gorenstein local ring of depth zero.
Denote by mod R the category of all finitely generated R-modules, and by the full …

The purpose of this paper is, as part of the stratification of Cohen–Macaulay rings, to
investigate the question of when the fiber products are almost Gorenstein rings. We show …

Let A be a Noetherian local ring with maximal ideal m. We assume that dim A= d> 0. The
local cohomology f unctor H~(-) was defined by Grothendieck [11] and he showed that for …

Let (R, 𝔪) be a commutative Noetherian local ring. It is known that R is Cohen–Macaulay if
there exists either a nonzero finitely generated R-module of finite injective dimension or a …

Gorenstein injective covers and envelopes over noetherian rings Page 1 PROCEEDINGS OF
THE AMERICAN MATHEMATICAL SOCIETY Volume 143, Number 1, January 2015, Pages …

Let R be a Gorenstein local ring with maximal ideal m satisfying m^3=0≠m^2. Set k=R/m
and e=rank_k(m/m^2). If e>2 and M, N are finitely generated R-modules, we show that the …

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 …

A complex C is called Gorenstein injective if there exists an exact sequence of
complexes⋯→ I− 1→ I0→ I1→⋯ such that each Ii is injective, C= Ker (I0→ I1) and the …