Let (R, m) be a local ring, and let C be a semidualizing R-module. In this paper, we are
concerned with the C-injective and GC-injective dimensions of certain local cohomology …

Let (R, m) be a commutative Noetherian local ring of Krull dimension d, and let C be a
semidualizing R-module. In this paper, it is shown that if R is complete, then C is a dualizing …

Let (R, 𝔪) be a commutative Noetherian local ring and M an R-module which is relative
Cohen-Macaulay with respect to a proper ideal 𝔞 of R, and set n:= ht M𝔞. We prove that …

Let be an ideal of ad-dimensional Gorenstein ring $ R $ and let $ M $ be an $ R $-module of
finite projective dimension. In this paper, among the other things, we show that, for every $ R …

Abstract Foxby (Math Scand 2: 175–186, 1971–1972) showed that a Cohen-Macaulay
module over a Gorenstein local ring has finite projective dimension if and only if its …

The notion of linkage with respect to a semidualizing module is introduced. This notion
enables us to study the theory of linkage for modules in the Bass class with respect to a …

Let (R, m) be commutative Noetherian local ring. It is shown that R is Cohen-Macaulay ring if
there exists a Cohen-Macaulay finite (ie finitely generated) R-module with finite upper …

Let 𝔞 be an ideal of a commutative Noetherian ring R and M and N two finitely generated R-
modules. Let cd𝔞 (M, N) denote the supremum of the i's such that. First, by using the theory …

Cohen-Macaulay dimension for modules over a commutative ring has been defined by AA
Gerko. That is a homological invariant sharing many properties with projective dimension …

Let (R, 𝔪) be a commutative Noetherian local ring. It is known that R is Cohen–Macaulay if
there exists either a nonzero finitely generated R-module of finite injective dimension or a …