We obtain various characterizations of commutative Noetherian local rings (R, m) in terms of
homological dimensions of certain finitely generated modules. Our argument has a series of …

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

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 …

If M is a nonzero finitely generated module over a commutative Noetherian local ring R such
that M has finite injective dimension and finite Gorenstein dimension, then it follows from a …

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 …

A new homological dimension, called G*-dimension, is defined for every finitely generated
module M over a local noetherian ring R. It is modeled on the CI-dimension of Avramov …

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 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 …

We prove that (a) if R is a commutative coherent ring, the weak global dimension of R equals
the supremum of the flat (or (FP–) injective) dimensions of the simple R-modules;(b) if R is …

Let $(R,\m) $ be a Noetherian local ring. Consider the notion of homological dimension of a
module, denoted H-dim, for H= Reg, CI, CI $ _* $, G, G $^* $ or CM. We prove that, if for a …