As the dual of the Auslander transpose and the resulting k-torsionfree module, the
cotranspose and k-cotorsionfree module with respect to a semidualizing bimodule have …

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 …

Let R and S be rings and RωS a semidualizing bimodule. We introduce and study the
adjoint cotransposes of modules and adjoint n-ω-cotorsionfree modules. We show that the …

In order to better unify the tilting theory and the Auslander–Reiten theory, Xi introduced a
general transpose called the relative transpose. Originating from this, we introduce and …

1. Introduction Throughout this paper, all rings are associative rings with units. For a ring R, we
use Mod R to denote the cate Page 1 EXTENSION CLOSURE OF ADJOINT COTORSIONFREE …

Let S and R be rings and _SC_R be a semidualizing bimodule. We first give the definitions
of C-transpose and nC-torsionfree and give a criterion for a module A to be G_C-projective …

Let $\mathcal X $ be a subcategory of left $ S $-modules and $ _ {R} U_ {S} $ an $(R, S) $-
bimodule. As a generalization of an adjoint cotranspose, we introduce an adjoint $\mathcal …

Assume that S is an almost excellent extension of R. Using functors Hom< sub> R(S,−) and—
⊗< sub> RS, we establish some connections between classes of modules [Figure not …

A right R-module UR is said to be cotilting if Cog (UR)=⊥ UR, where⊥ UR= KerExt1R (, U).
So cotilting modules generalize injective cogenerators. If U is cotilting, then T=(KerHom …

In this paper we study cotorsion and torsion pairs induced by cotilting modules. We prove
the existence of a strong relationship between the Σ-pure-injectivity of the cotilting module …