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 …

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 present results on reflexive modules over Gorenstein rings which generalize results of
Serre and Samuel on reflexive modules over regular local rings. We characterize Gorenstein …

Let R be a commutative Noetherian ring. It is shown that the finitely generated R-module M
with finite Gorenstein dimension is reflexive if and only if M p is reflexive for p∈ Spec (R) …

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 …

EXISTENCE OF TOTALLY REFLEXIVE MODULES VIA GORENSTEIN HOMOMORPHISMS
tion S-+ S/(xt,··· ,xn) ~ R, with Xt, ··· ,xn an S-reg Page 1 JOURNAL OF COMMUTATIVE …

Let R be a commutative Noetherian local Gorenstein ring with residue field k. We show that
G (k), the Gorenstein injective envelope of k, is an artinian R-module, and we compute G (k) …

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 …

We give some criteria for projectivity of reflexive modules in this paper. In the second
section, we show that a reflexive module M over a regular local ring R is free if …

It is proved that the minimal free resolution of a module M over a Gorenstein local ring R is
eventually periodic if, and only if, the class of M is torsion in a certain Z [t±1]-module …