For finite modules over a local ring and complexes with finitely generated homology, we
consider several homological invariants sharing some basic properties with projective …

Our purpose in this work is multifold. First, we provide general criteria for the finiteness of the
projective and injective dimensions of a finite module $ M $ over a (commutative) …

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 …

Given a semidualizing module C over a commutative Noetherian ring, Holm and Jørgensen
[Semi-dualizing modules and related Gorenstein homological dimensions, J. Pure Appl …

Let R be a semiperfect commutative Noetherian ring with identity and C, S be semidualizing
R-modules. We study the theory of linkage with respect to S for modules of finite GC …

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 …

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

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

For finitely generated module $ M $ over a local ring $ R $, the conventional notions of
complete intersection dimension $\cid_R M $ and Cohen-Macaulay dimension $\cmdim_R …

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 …