… In this paper, we prove that the Bass class BC (S) with respect to a semidualizing bimodule
C contains all FP-injective S-modules. We introduce the definition of C-FPinjective modules, …

… a semidualizing bimodule. All R- or S-modules are understood to be left R- or S-modules. …
Theorem 1.1 Let SCR be a faithfully semidualizing bimodule and na non-negative integer. …

… of such modules and the structure of the entire set of isomorphism classes of semidualizing
R-modules, … First, taking our cues from [9], we describe the semidualizing modules over a …

… modules with respect to a semidualizing bimodule In this section, we introduce and investigate
properties of the totally reflexive module with respect to a semidualizing bimodule SCR …

… or C⊗D-covers) of modules, which allows us to apply known results on the existence of
envelopes and covers to those related to semidualizing R-modules. For example, we prove that: (…

… a faithfully semidualizing bimodule, we give some equivalent characterizations of left n-coherent
rings in terms of C-FP n -flat left S-modules and C-FP n -injective left R-modules. Finally, …

… of modules. When S C R is a faithfully semidualizing bimodule, we study the Foxby …
between the subclasses of the Auslander class and that of the Bass class with respect to C. …

… Let R and S be rings and S CR a faithfully semidualizing bimodule. A left S-module M is
called Ding C-projective if there exists an exact sequence of C-projective left S-modules …

… In this section, we extend the notion of “k-th syzygy” and “k-torsionless” module to the relative
setting with respect to a semidualizing module. As an application, we employ the two new …

… -weak injective modules with respect to a semidualizing bimodule SCR, where R and S are
arbitrary associative rings. It is proven that the class of GC-weak injective modules is closed …