We prove a generalization to the context of topological tilting modules of the fact that a tilting
module is faithfully balanced and also a tilting module over its endomorphism ring. Some …

Tilting modules appear in a variety of ways: their first definition was in the context of finite
dimensional algebras over a field. Later, they appeared naturally in applications of the …

In a compactly generated triangulated category, we introduce a class of tilting objects
satisfying a certain purity condition. We call these the decent tilting objects and show that the …

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 …

Abstract Let E=(A, S) be an exact category with enough projectives P. We introduce the
notion of support τ-tilting subcategories of E. It is compatible with the existing definitions of …

Let TR be a 1-tilting module with tilting torsion pair (Gen T, F) in Mod-R. The following
conditions are proved to be equivalent:(1) T is pure projective;(2) Gen T is a definable …

The aim of this note is to develop a construction of tilting complexes given by Okuyama [4]
and a construction of two-sided tilting complexes given by Rouquier and Zimmermann [7] …

The paper surveys several generalizations of the notion of a cotilting module over an Artin
algebra to more general rings. Classically, a module U over an Artin algebra Λ is a cotilting …

In Corollary 4.2 we showed that for subcategories C of mod II closed under extensions of the
form C= Sub M there are only a finite number of nonisomorphic indecomposable objects in …

Tilting modules are an essential tool of representation theory and have been studied by
several authors. In the present paper we state an existence theorem for tilting modules …