On tau-Extending Modules


Ceken S., ALKAN M.

MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.9, no.1, pp.129-142, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 1
  • Publication Date: 2012
  • Doi Number: 10.1007/s00009-010-0096-2
  • Journal Name: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.129-142
  • Keywords: tau-large submodule, tau-closed submodule, extending module, tau-complemented module, tau-CS module
  • Akdeniz University Affiliated: Yes

Abstract

Motivated by [2] and [6], we introduce a generalization of extending (CS) modules by using the concept of tau-large submodule which was defined in [9]. We give some properties of this class of modules and study their relationship with the familiar concepts of tau-closed, tau-complement submodules and the other generalization of extending modules (tau-complemented, tau-CS, s-tau-CS modules). We are also interested in determining when a tau-divisible module is tau-extending. For a tau-extending module M with C3, we obtain a decomposition theorem that there is a submodule K of M such that M = tau(M) circle plus K and K is tau (M)-injective. We also treat when a direct sum of tau-extending modules is tau-extending.