ABSOLUTE CO-SUPPLEMENT AND ABSOLUTE CO-COCLOSED MODULES


Tutuncu D. K., Toksoy S. E.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.42, no.1, pp.67-79, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 1
  • Publication Date: 2013
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.67-79
  • Hacettepe University Affiliated: Yes

Abstract

A module M is called an absolute co-coclosed (absolute co-supplement) module if whenever M congruent to T/X the submodule X of T is a coclosed (supplement) submodule of T. Rings for which all modules are absolute co-coclosed (absolute co-supplement) are precisely determined. We also investigate the rings whose (finitely generated) absolute co-supplement modules are projective. We show that a commutative domain R is a Dedekind domain if and only if every submodule of an absolute co-supplement R-module is absolute co-supplement. We also prove that the class Coclosed of all short exact sequences 0 -> A -> B -> C -> 0 such that A is a coclosed submodule of B is a proper class and every extension of an absolute co-coclosed module by an absolute co-coclosed module is absolute co-coclosed.