For finitely generated modules $ M $ and $ N $ over a commutative Noetherian local ring $
R $, we give various sufficient criteria for detecting freeness of $ M $ or $ N $ via vanishing …

For a finitely generated module M over a commutative Noetherian ring R, we settle the
Auslander–Reiten conjecture when at least one of Hom R (M, R) and Hom R (M, M) has …

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 …

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 C be a semidualizing module for a commutative ring R. In this paper, we study the
resulting modules of finite GC-projective dimension in Bass class, showing that they admit …

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) …

Modules of finite homological dimension with respect to a semidualizing module Page 1
Arch. Math. 93 (2009), 111–121 c© 2009 Birkhäuser Verlag Basel/Switzerland 0003-889X/09/020111-11 …

Let R be a commutative Noetherian local ring and M, N be finitely generated R-modules. We
prove a number of results of the form: if Hom R (M, N) has some nice properties and Ext R …

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