We show that, if T is a selfsmall and selforthogonal module over a noetherian ring R of finite
global dimension with the endomorphism ring A, then fdTA⩽ gdA⩽ idRT+ fdTA. Applying the …

For a left module M over a ring R, pd (M) and id (M) denote the projective and injective
dimension of M, respectively. A (left and right) noether ring R is called n-Gorenstein for an n> …

In this paper, we study injective dimension and Gorenstein injective dimension over local
ring homomorphisms. Some well-known results are generalized. For example, the Bass …

A fintitely generated R-module C is semidualizing if R= HomR (C, C) and [special charactes
omitted](C, C)= 0. In this dissertation we build off of Takahashi and White's P C-projective …

Let R be a local ring and M a finitely generated R-module. The complete intersection
dimension of M–defined by Avramov, Gasharov and Peeva, and denoted–is a homological …

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 …

1. Introduction. Given the R-module A, we define the strong injective dimension and its dual
the strong projective dimension of A.(Our notations are Sid (A) and Spd (A) respectively.) …

Let R be a commutative Noetherian ring and let M be a finite (that is, finitely generated) R-
module. The notion grade of M, grade M, has been introduced by Rees as the least integer …

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 …

A Bass equality for Gorenstein injective dimension of modules finite over homomorphisms |
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