Let R be a commutative Noetherian ring with identity and C a semidualizing module for R.
Let 𝒫 C (R) and ℐ C (R) denote, respectively, the classes of C-projective and C-injective R …

Let $ A $ be a ring, and let $ M $ and $ N $ be $ A $-modules. Then $ N $ can be viewed as
a group object in the category $ A $-Mod/$ M $ of $ A $-modules over $ M $ and Ext $^ 1 (M …

In this paper, we discuss the Bass class and the Auslander class with respect to a
semidualizing module over an associative ring. Let _SC_R be a semidualizing module, we …

Let R be a commutative ring, 𝒞 be a semidualizing R-module. We show that the Auslander
class 𝒜𝒞 (R) with respect to 𝒞 is the first left orthogonal class of some pure injective module …

Let C be a semidualizing module over a commutative noetherian ring R. We exhibit an
isomorphism Tor^F_CM_i(-,-)≅Tor^P_CM_i(-,-) between the bifunctors defined via C-flat and …

Let R and S be rings and RωS a semidualizing bimodule. We investigate when the double
functor TorS i (ω, Exti R (ω,−)) preserves epimorphisms and the double functor Exti R (ω …

Let C be a semidualizing R-module, where R is a commutative ring. We first introduce the
definition of C-cotorsion modules, and obtain the properties of C-cotorsion modules. As …

Let R be a commutative Cohen–Macaulay ring, and let C be a semidualizing module of R. In
this paper, we show that C is generically dualizing if and only if the tensor products of …

Let $ R $ be a Noetherian ring and let $ C $ be a semidualizing $ R $-module. In this paper,
we are concerned with the tensor and torsion product of $ C $-injective modules. Firstly, it is …

Let R be a ring (not necessarily commutative). A left R-module is said to be cotorsion if Ext 1
R (G, M)= 0 for any flat R-module G. It is well known that each pure-injective left R-module is …