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 …

Let S be a deeply embedded, equicharacteristic, Artinian Gorenstein local ring. We prove
that if R is a non-Gorenstein quotient of S of small colength, then every totally reflexive R …

We introduce the notion of relative singularity category with respect to a self‐orthogonal
subcategory ω of an abelian category. We introduce the Frobenius category of ω‐Cohen …

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 …

We give counterexamples to the following conjecture of Auslander: given a finitely
generated module M over an Artin algebra Λ, there exists a positive integer nM such that for …

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

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 …

Let R be a commutative noetherian local ring that is not Gorenstein. It is known that the
category of totally reflexive modules over R is representation infinite, provided that it …

We construct a class of Gorenstein local rings R which admit minimal complete R-free
resolutions C such that the sequence {rank R Ci} is constant for i< 0, and grows …

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 …