In this paper, we show the existence of copure injective preenvelopes over noetherian rings
and copure flat preenvelopes over commutative artinian rings. We use this to characterize …

We characterize left Noetherian rings in terms of the duality property of injective
preenvelopes and flat precovers. For a left and right Noetherian ring R, we prove that the flat …

In this paper, we show that if R is a local Cohen–Macaulay ring admitting a dualizing module
Ω, then Ω-Gorenstein projective and flat covers and Ω-Gorenstein injective envelopes exist …

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 commutative noetherian local ring and consider the set of isomorphism classes of
indecomposable totally reflexive R-modules. We prove that if this set is finite, then either it …

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 …

Throughout this paper, R will denote a commutative noetherian ring. If M is an R-module, we
can construct an injective resolvent of M using injective precovers (see Enochs [5]). If we use …

Let R be a commutative noetherian local ring. A finitely generated R-module C is
semidualizing if it is self-orthogonal and\rm Hom _R (C, C) ≅ R. We prove that a Cohen …

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 …

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 …