Lifting modules with indecomposable decompositions


Er N. F. , Ertas N. O.

COMMUNICATIONS IN ALGEBRA, vol.36, no.2, pp.395-404, 2008 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 2
  • Publication Date: 2008
  • Doi Number: 10.1080/00927870701715738
  • Title of Journal : COMMUNICATIONS IN ALGEBRA
  • Page Numbers: pp.395-404

Abstract

A module M is called a "lifting module" if, any submodule A of M contains a direct summand B of M such that A/B is small in M/B. This is a generalization of projective modules over perfect rings as well as the dual of extending modules. It is well known that an extending module with ascending chain condition (a.c.c.) on the annihilators of its elements is a direct sum of indecomposable modules. If and when a lifting module has such a decomposition is not known in general In this article, among other results, we prove that a lifting module M is a direct sum of indecomposable modules if (i) rad(M((I))) is small in M((I)) for every index set I, or, (ii) M has a.c.c. on the annihilators of (certain) elements, and rad(M) is small in M.