Rad-circle plus-Supplemented Modules and Cofinitely Rad-circle plus-Supplemented Modules


Ecevit S., Kosan M. T. , Tribak R.

ALGEBRA COLLOQUIUM, vol.19, no.4, pp.637-648, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 4
  • Publication Date: 2012
  • Doi Number: 10.1142/s1005386712000508
  • Journal Name: ALGEBRA COLLOQUIUM
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.637-648
  • Keywords: cofinite submodules, local modules, w-local modules, (cofinitely) Rad-circle plus-supplemented modules
  • Gazi University Affiliated: No

Abstract

A module M is called (cofinitely) Rad-circle plus-supplemented if every (cofinite) submodule of M has a Rad-supplement that is a direct summand of M. We prove that if M is a coatomic cofinitely Rad-circle plus-supplemented module, then M is an irredundant sum of local direct summands. We show that the classes of cofinitely Rad-circle plus-supplemented modules and Rad-circle plus-supplemented modules are closed under finite direct sums. We also show that every direct summand of a weak duo (cofinitely) Rad-circle plus-supplemented module is (cofinitely) Rad-circle plus-supplemented.