We establish the global analogues of some dualities and equivalences in local algebra by
developing the theory of relative Cohen–Macaulay modules. Let R be a commutative …

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,\fm) $ be a relative Cohen-Macaulay local ring with respect to an ideal $\fa $ of $ R $
and set $ c:=\h\fa $. In this paper, we investigate some properties of the Matlis dual $\H …

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 …

ON THE NON-VANISHING AND THE ARTINIANNESS OF GENERALIZED LOCAL
COHOMOLOGY MODULES Page 1 Journal of Algebra and Its Applications Vol. 12, No. 4 (2013) …

Let R be a commutative Noetherian ring with nonzero identity, 𝔞 an ideal of R, M a finite R–
module, X an arbitrary R–module, and na non-negative integer. Here, we show that, in the …

Let R be a Cohen–Macaulay local ring. In this paper, we study the structure of Ulrich R-
modules mainly in the case where R has minimal multiplicity. We explore generation of …

We introduce a generalization of the formal local cohomology module, which we call a
formal local cohomology module with respect to a pair of ideals, and study its various …

Let $(R,\underline {m}) $ be a commutative Noetherian local ring and $ M $ be a non-zero
finitely generated $ R $-module. We show that if $ R $ is almost Cohen-Macaulay and $ M …

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 …