Throughout this note we assume that R is a commutative ring with identity and all R-modules
are unital. Let (T, F) bea torsion theory orR-mod. We call that T (F) is completely reducible …

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 study torsionfree and divisible dimensions in terms of right derived functors of-⊗-. We
also investigate the cotorsion pair cogenerated by the class of cyclic torsionfree right R …

Let R be a ring and let R-mod denote the category of all left R-modules. If T is a (hereditary)
torsion theory on R-mod then a left R-module M is said to have a T-composition series if and …

Hereditary Cotilting Modules Page 1 Ž . Journal of Algebra 238, 462478 2001 doi:10.1006rjabr.2000.8621,
available online at http:rrwww.idealibrary.com on Hereditary Cotilting Modules Francesca …

JP Jans has shown that if a ring R is right perfect, then a certain torsion in the category Mod
R of left R-modules is closed under taking direct products. Extending his method, JS Alin …

Coherent rings relative to (hereditary) torsion theories have been studied in several papers.
The characterization, given by Cateforis I41, of nonsingular rings with flat maximal quotient …

A result of L. Angeleri Hügel in [A key module over pure-semisimple hereditary rings, J.
Algebra 307 (2007), 361-376] asserts that if R is a left pure semisimple hereditary ring, then …

Let R be a ring and n, k be two non-negative integers. As an extension of several known
notions, we introduce and study (n, k)-weak cotorsion modules using the class of right R …

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 …