In this paper, we define a homological invariant for finitely generated modules over a
commutative noetherian local ring, which we call upper Cohen-Macaulay dimension. This …

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 …

A new homological dimension, called GCM-dimension, will be defined for any finitely
generated module M over a local Noetherian ring R. GCM-dimension (short for Generalized …

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 …

We define three new homological dimensions: Cohen-Macaulay injective, projective, and
flat dimension, and show that they inhabit a theory similar to that of classical injective …

We introduce new homological dimensions, namely the Cohen-Macaulay projective,
injective and flat dimensions for homologically bounded complexes. Among other things we …

We define three new homological dimensions-Cohen-Macaulay injective, projective, and flat
dimension-which inhabit a theory similar to that of classical injective, projective, and flat …

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 (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 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 …