Let R be a ring. We prove that the homotopy category K (R-Proj) is always \aleph_1-
compactly generated, and, depending on the ring R, it may or may not be compactly …

By the Telescope Conjecture for Module Categories, we mean the following claim:“Let R be
any ring and (A, B) be a hereditary cotorsion pair in Mod-R with A and B closed under direct …

Chase has given several characterizations of a right coherent ring, among which are: every
direct product of copies of the ring is left-flat; and every finitely generated submodule of a …

In his paper [191 Morita introduced the concept of functorial dualities between two full
subcategories A& and.+? of the categories of right R-modules and left S-modules containing …

In [H. Krause, O. Solberg, Applications of cotorsion pairs, J. London Math. Soc. 68 (2003)
631–650], the Telescope Conjecture was formulated for the module category ModR of an …

CHAPTER 1 1.1 Introduction The purpose of this thesis is to continue the investi gation of
general torsion theories and torsion classes and also to investigate certain specific torsion …

The torsion products To&M, N) are defined when M and N are respectively right and left
modules over an associative ring n with identity element, and s 2 0 [4]. We give a new …

This article introduces the concept of μ-complemented modules as follows: given a
hereditary torsion theory in Mod-R with associated torsion functor μ we say that a module M …

To a big-tilting object in a complete, cocomplete abelian category with an injective
cogenerator we assign a big-cotilting object in a complete, cocomplete abelian category with …

Let R be a general ring. Duality pairs of R-modules were introduced by Holm-Jørgensen.
Most examples satisfy further properties making them what we call semi-complete duality …