When some complement of a z-closed submodule is a summand


KARA ŞEN Y. , TERCAN A.

COMMUNICATIONS IN ALGEBRA, vol.46, no.7, pp.3071-3078, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 7
  • Publication Date: 2018
  • Doi Number: 10.1080/00927872.2017.1404080
  • Title of Journal : COMMUNICATIONS IN ALGEBRA
  • Page Numbers: pp.3071-3078
  • Keywords: C-11-module, complement submodule, extending module, z-closed submodule, MODULES

Abstract

In this article we study modules with the condition that every z-closed submodule has a complement which is a direct summand. This new class of modules properly contains the class of extending modules. It is well known that the class of extending modules is closed under direct summands, but not under direct sums. In contrast to extending (or CS) modules, it is shown that the class of modules with former property is closed under direct sums. However we provide number of algebraic topological examples which show that this new class of modules is not closed under direct summands. To this end we obtain several results on the inheritance of the latter closure property.