Foxby duality has proven to be an important tool in studying the category of modules over a
local Cohen-Macaulay ring admitting a dualizing module. Recently the notion of a semi …

An additive functor from the category of flat right R‐modules to the category of abelian
groups is continuous if it is isomorphic to a functor of the form−⊗ RM, where M is a 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 …

For a module-finite algebra over a commutative noetherian ring, we give a complete
description of flat cotorsion modules in terms of prime ideals of the algebra, as a …

We study the notion (for categories of modules) dual to that of torsion radical and its
connections with projective modules. Torsion radicals in categories of modules have been …

A cotorsion theory is defined as a pair of classes Ext-orthogonal to each other. We give a
hereditary condition (HC) which is satisfied by the (flat, cotorsion) cotorsion theory and give …

Let R be a ring, na fixed nonnegative integer and In (Fn) the class of all left (right) R-modules
of injective (flat) dimension at most n. A left R-module M (resp., right R-module F) is called n …

The aim of this paper is to describe the classes of strongly flat and weakly cotorsion modules
with respect to a multiplicative subset or a finite collection of multiplicative subsets in a …

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 …

We introduce the notion of a duality pair and demonstrate how the left half of such a pair is"
often" covering and preenveloping. As an application, we generalize a result by Enochs et …