We consider local non-Gorenstein rings of the form $(S_i,\mathfrak {n} _i)= k [X, Y_1,\ldots,
Y_i]/\left (X^ 2,(Y_1,\ldots, Y_i)^ 2\right), $ where $ i\geq 2. $ We show that every totally …

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 …

Abstract We study Cohen–Macaulay non-Gorenstein local rings (R, m, k) admitting certain
totally reflexive modules. More precisely, we give a description of the Poincaré series of k by …

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) …

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 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 …

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 R be a commutative Noetherian ring and let C be a semidualizing R-module. It is shown
that a finitely generated R-module M with finite GC-dimension is C-reflexive if and only if M 𝔭 …

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 …