GOLDIE EXTENDING MODULES

AKALAN E., Birkenmeier G. F., TERCAN A.

COMMUNICATIONS IN ALGEBRA, vol.37, no.2, pp.663-683, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 2
  • Publication Date: 2009
  • Doi Number: 10.1080/00927870802254843
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.663-683
  • Hacettepe University Affiliated: Yes

Abstract

In this article, we de. ne a module M to be G-extending if and only if for each X <= M there exists a direct summand D of M such that X boolean AND D is essential in both X and D. We consider the decomposition theory for G-extending modules and give a characterization of the Abelian groups which are G-extending. In contrast to the characterization of extending Abelian groups, we obtain that all finitely generated Abelian groups are G-extending. We prove that a minimal cogenerator for Mod-R is G-extending, but not, in general, extending. It is also shown that if M is (G-) extending, then so is its rational hull. Examples are provided to illustrate and delimit the theory.