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 (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 …

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 …

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 (R, 𝔪) be a commutative Noetherian local ring. In this paper we prove that if R admits a
finite module of finite Gorenstein injective dimension and maximal Krull dimension then R is …

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 be a commutative Noetherian ring. If cmd R≤ 1, then it is shown that for any R-module
the large restricted injective dimension is a refinement of the Gorenstein injective dimension …

Let $ I $ be an integrally closed ideal in a commutative Noetherian ring $ A $. Then the local
ring $ A_ {\mathfrak {p}} $ is regular (resp. Gorenstein) for every $\mathfrak {p}\in\mathrm …

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 …

We obtain various characterizations of commutative Noetherian local rings $(R,\fm) $ in
terms of homological dimensions of certain finitely generated modules. For example, we …