Let R and S be rings and _SC_R 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 …

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 …

We extend the definition of a semidualizing module to general associative rings. This
enables us to define and study Auslander and Bass classes with respect to a semidualizing …

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

This is a study of Ding projective modules relative to a semidualizing module and related
topics. Firstly, we study DC-projective dimensions and DC-projective modules under change …

An R-module M is called Ding projective if there exists an exact sequence⋯→ P1→ P0→
P0→ P1→⋯ of projective R-modules with M= Ker (P0→ P1) such that Hom (-, F) leaves the …

Abstract Let R⋉ M be a trivial extension of a ring R by an RR-bimodule M such that MR,
RM,(R, 0) R⋉ M and R⋉ M (R, 0) have finite flat dimensions. We prove that (X, α) is a Ding …

Let $ S $ and $ R $ be rings and $ _SC_R $ a (faithfully) semidualizing bimodule. We
introduce and study $ C $-weak flat and $ C $-weak injective modules as a generalization of …

A submodule N of a module M is called ${\mathcal {S}} $-closed (in M) if M/N is nonsingular.
It is well-known that the class Closed of short exact sequences determined by closed …

In this paper, we introduce and discuss the notion of DC-projective modules over
commutative rings, where C is a semidualizing module. This extends Gillespie and Ding …