In this paper we assume that $ R $ is a Gorenstein Noetherian ring. We show that if
$(R,\mathfrak {m}) $ is also a local ring with Krull dimension $ d $ that is less than or equal to …

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 …

Let A be a commutative local Noetherian ring with identity of Krull dimension n, m its
maximal ideal. Sharp has proved that if A is Cohen-Macauley and a homomorphic image of …

In this paper, we study Gorenstein injective modules over a local Noetherian ring R. For an
R-module M, we show that M is Gorenstein injective if and only if Hom R (Ȓ, M) belongs to …

R will denote an n-Gorenstein ring, that is, R is left and right noetherian with injective
dimension at most n on either side. R module will mean a left R-module and all modules will …

We prove that the class of Gorenstein injective modules is both enveloping and covering
over a two sided noetherian ring such that the character modules of Gorenstein injective …

In this paper we are going to develop a theory of Gorensteinness in graded rings associated
to certain filtrations of ideals in Gorenstein local rings. Let A be a Cohen–Macaulay local ring …

Let R be a commutative Noetherian ring and let I be an ideal of R. In this paper, we study the
amalgamated duplication ring R⋈ I which is introduced by D'Anna and Fontana. It is shown …

Let (R, 𝔪) be a commutative Noetherian local ring and M an R-module which is relative
Cohen-Macaulay with respect to a proper ideal 𝔞 of R, and set n:= ht M𝔞. We prove that …

In this article we extend the notion of Gorenstein injective and projective modules to that of
complexes and characterize such complexes. We prove that over an n-Gorenstein ring every …