The notion of a canonical module of a (noetherian) local ring is due to Grothendieck, who
called it a module of dualizing differentials (cf.[5, p. 94]). The term" a canonical module" was …

Let R be a Cohen–Macaulay local ring. It is shown that under some mild conditions, the
Cohen–Macaulay property is preserved under linkage. We also study the connection of the …

Let R be a Cohen–Macaulay local ring. We prove that the n th syzygy module of a maximal
Cohen–Macaulay R-module cannot have a semidualizing direct summand for every n≥ 1 …

Let $ R $ be a commutative noetherian local ring, and let $ M $ be a finitely generated $ R $-
module. Inspired by works of Vasconcelos and Briggs on characterization of complete …

Let (R, m) denote a commutative Noetherian local ring and let M be a finite R-module. In this
paper, we study relative Cohen-Macaulay rings with respect to a proper ideal a of R and …

Let $ S $ be an unramified regular local ring having mixed characteristic $ p> 0$ and $ R $
the integral closure of $ S $ in a $ p $ th root extension of its quotient field. We show that $ R …

Let (R, m) be a relative Cohen–Macaulay local ring with respect to an ideal a of R and set c
to be ht a. We investigate some properties of the Matlis dual of the R-module H ac (R), and …

Let $(R,\mathfrak {m}) $ be a local ring and $ I $ be an $\mathfrak {m} $-primary ideal such
that ${\dim _k}(I/I\mathfrak {m})= l $, where $ k= R/\mathfrak {m} $. Denote the associated …

In [4] and [5] M. Hochster introduced the notion of amiability for a system of parameters in a
local noetherian ring (see also the definition in 3). The existence of amiable systems of …

It is known that the i-th local cohomology of a finitely generated R-module M over a positively
graded commutative Noetherian ring R, with respect to the irrelevant ideal R+ is graded …