The Existence of Finitely Generated Modules of Finite Gorenstein Injective Dimension Page 1
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 134, Number 11 …

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 (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. In this paper we prove that if R admits a
finite module of finite Gorenstein injective dimension and maximal Krull dimension then R is …

Let $ R $ be a commutative Noetherian local ring. We show that $ R $ is Gorenstein if and
only if every finitely generated $ R $-module can be embedded in a finitely generated $ R …

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 …

We study some aspects of distinguished finitely generated modules of finite injective
dimension. Following Bass' conjecture, this implies that the ring is Cohen-Macaulay. 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 …

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 be a commutative noetherian henselian non-Gorenstein local ring of depth zero.
Denote by mod R the category of all finitely generated R-modules, and by the full …