Let R, S be arbitrary associative rings and RCS a semidualizing bimodule. We give some
equivalent characterizations for R being left coherent (and right perfect) rings, left …

Let R be a commutative ring and C a semidualizing R-module. We investigate the relations
between C-flat modules and C-FP-injective modules and use these modules and their …

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 …

Let S and R be rings, SCR be a semidualizing bimodule and n≥ 0 be an integer or n=∞.
We introduce and study C-FP n-injective and C-FP n-flat modules as a common …

Let C be a class of some finitely presented left R-modules. A left R-module M is called C-
injective, if Ext R 1 (C, M)= 0 for each C∈ C. A right R-module M is called C-flat, if Tor 1 R …

Let R be a ring. A right R-module A is said to be C-flat if the kernel of any epimorphism B→ A
is C-pure in B, ie the induced map Hom (C, B)→ Hom (C, A) is surjective for any cyclic right …

Let R be a commutative ring. We define and study f-projective modules with respect to a
semidualizing R-module C, which are called C–f-projective modules. As consequences, we …

We characterize left coherent, left Noetherian, and left Artinian rings by the flatness,
projectivity, and injectivity of the character module of certain left/{-modules. Introduction. The …

In this paper, we characterize strongly right C 2-rings in terms of finite-direct-injective
modules which is a generalization of direct-injective modules (or C 2-modules). Using this …

Given an R-module C and a class of R-modules 𝒟 over a commutative ring R, we investigate
the relationship between the existence of 𝒟-envelopes (respectively, 𝒟-covers) and the …