We study the concepts of the 𝒫 C-projective and the ℐ C-injective dimensions of a module in
the noncommutative case, weakening the condition of C being semidualizing. We give the …

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 and S be rings and RCS a semidualizing bimodule. We show that the supremum of the
C-projective dimensions of C-flat left R-modules is less than or equal to that for left R …

Let R be a left and right Noetherian ring and C a semidualizing R-bimodule. We introduce a
transpose Tr c M of an R-module M with respect to C which unifies the Auslander transpose …

Let R be a commutative (possibly non-Noetherian) ring (in order to make things less
technical) and C a semidualizing R-module. In this article, we introduce and investigate the …

Let X be a class of left R-modules, Y be a class of right R-modules. In this article, we
introduce and study Gorenstein (X, Y)-flat modules as a common generalization of some …

Let R be a ring, C be a left R-module and S= End R (C). When C is semidualizing, the
Auslander class AC (S) and the Bass class ℬ C (R) associated with C have been the subject …

As a generalization of a resolving subcategory, which was introduced by Auslander and
Bridger in [2], the notion of a quasi-resolving subcategory of an abelian category is …

Recently, Gorenstein dimensions relative to a semidualizing module have been the subject
of numerous studies with interesting extensions of the classical homological dimensions …

This paper aims at generalizing the notions of “Auslander dual”,“k-torsionless” and “k-th
syzygy” modules to the relative setting with respect to a semidualizing module. It is shown …