Khaled Al-Takhman, Christian Lomp, Robert Wisbauer, “$\tau$-complemented and $\tau$-supplemented modules”, Algebra Discrete Math., 2006, Issue 3,Pages 1

This article is cited in 11 papers

RESEARCH ARTICLE

$\tau$-complemented and $\tau$-supplemented modules

Khaled Al-Takhman^a, Christian Lomp^b, Robert Wisbauer^c

^a Department of Mathematics, Birzeit University, Birzeit P. . Box 14, Palestine
^b Centro de Matematica da Universidade do Porto, 4169–007 Porto, Portugal
^c Mathematisches Institut der, Heinrich-Heine Universität, 0225 Düsseldorf, Germany

Abstract: Proper classes of monomorphisms and short exact sequences were introduced by Buchsbaum to study relative homological algebra. It was observed in abelian group theory that complement submodules induce a proper class of monomorphisms and this observations were extended to modules by Stenström, Generalov, and others. In this note we consider complements and supplements with respect to (idempotent) radicals and study the related proper classes of short exact sequences.

Keywords: proper classes; neat and coneat submodules; $\tau$-supplemented, $\tau$-complemented and $\tau$-semiperfect modules.

MSC: 16D90, 16E50, 16.E99

Received: 16.01.2006
Revised: 21.11.2006

Language: English