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 be a commutative Noetherian (not necessary local) ring with identity and a be a proper
ideal of R. We introduce a notion of a-relative system of parameters and characterize them …

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 M be an R-module over a Noetherian ring R and 𝔞 an ideal of R with c= cd (𝔞, R). First,
over an 𝔞-relative Cohen–Macaulay local ring (R, 𝔪), we provide a characterization of the 𝔞 …

The study of rings and modules with homological criteria is a cornerstone of commutative
algebra. Let $ R $ be a commutative Noetherian ring with identity (not necessarily local) and …

Let $ R $ be a commutative Noetherian ring with identity (not necessarily local) and $\frak a
$ a proper ideal of $ R $. We study the invariance of some classes of $\frak a $-relative …

Throughout this paper, is a commutative Noetherian ring and is a proper ideal of. In the case
where is local with maximal ideal, denotes the-adic completion of,⁄ denotes the injective hull …

Introduction Throughout this paper, R is a commutative Noetherian ring and a is a proper
ideal of R. In the case where R is local with maximal ideal m, R denotes the m-adic …

Let a be a proper ideal of a ring R. A finitely generated R-module M is said to be a-relative
generalized Cohen-Macaulay if f_a (M)= cd (a, M). In this note, we introduce a suitable …