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Torsion-Free and Divisible Modules Over Finite-Dimensional Algebras

Published online by Cambridge University Press:  20 November 2018

F. Okoh
F. Okoh*
Affiliation:
Department of Mathematics, Wayne State University, Detroit, Michigan 48202, U.S.A.
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Abstract

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If R is a Dedekind domain, then div splits i.e.; the maximal divisible submodule of every R-module M is a direct summand of M. We investigate the status of this result for some finite-dimensional hereditary algebras. We use a torsion theory which permits the existence of torsion-free divisible modules for such algebras. Using this torsion theory we prove that the algebras obtained from extended Coxeter- Dynkin diagrams are the only such hereditary algebras for which div splits. The field of rational functions plays an essential role. The paper concludes with a new type of infinite-dimensional indecomposable module over a finite-dimensional wild hereditary algebra.

Keywords

16D7016G6013C12
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 1 , 01 March 1996 , pp. 111 - 114
Copyright
Copyright © Canadian Mathematical Society 1995

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