Let R be a commutative Noetherian ring, and let C be a semidualizing R-module. The notion
of C-tilting R-modules is introduced as the relative setting of the notion of tilting R-modules …

We introduce symmetric subcategories of abelian categories and show that the derived
category of the endomorphism ring of any good tilting module over a ring is a recollement of …

Relative cotilting modules and their connection to ordinary cotilting modules were first
studied by Auslander and Solberg in [6] and [7]. Among other things, they show that relative …

An important result in tilting theory states that a class of modules over a ring is a tilting class
if and only if it is the Ext-orthogonal class to a set of compact modules of bounded projective …

In commutative ring theory, the notion of Gorenstein rings has been studied widely. For rings
having finite Krull dimension, Bass showed the characterization of Gorenstein rings as rings …

Let M be a module over an associative ring R and σ [M] the category of M-subgenerated
modules. Generalizing the notion of a projective generator in σ [M], a module P∈ σ [M] is …

In this article, we prove a similar theorem to C, Theorem 6 which holds in a more general
setting. In particular, we focus on the construction of a natural morphism giving rise to a …

This book provides a unified approach to much of the theories of equivalence and duality
between categories of modules that has transpired over the last 45 years. In particular …

Tilting modules, generalising the notion of progenerator, furnish equivalences between
pieces of module categories. This paper is dedicated to study how much these pieces say …