MODULES THAT HAVE A WEAK delta-SUPPLEMENT IN EVERY TORSION EXTENSION

Sozen E. O., Eryilmaz F., Eren S.

JOURNAL OF SCIENCE AND ARTS, no.2, pp.269-274, 2017 (ESCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2017
  • Journal Name: JOURNAL OF SCIENCE AND ARTS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.269-274
  • Keywords: delta-small submodule, weak delta-supplement, torsion extension
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

We study modules with the properties (delta-TWE) and (delta-TWEE) which are adopted Zoschinger's modules with the properties (E) and (EE). We call a module (delta-TWE) module if M has a weak delta-supplement in every torsion extension. Similarly if M has ample weak delta-supplements in every torsion extension then M is called (delta-TWEE) module. We obtain various properties of these modules. We will show that (1) Every direct summand of a (delta-TWE) module is a (delta-TWE) module. (2) A module M has the property (delta-TWEE) iff every submodule of M has the property (delta-TWE). (3) Any factor module of a (delta-TWE) module is a (delta-TWE) module under a special condition. (4) Over a non local ring, if every submodule of a module M is a (delta-TWE) module, then it is cofinitely weak delta-supplemented.