Generalizations of circle plus-supplemented modules

Turkmen B. N., Pancar A.

UKRAINIAN MATHEMATICAL JOURNAL, vol.65, no.4, pp.612-622, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 65 Issue: 4
  • Publication Date: 2013
  • Doi Number: 10.1007/s11253-013-0799-1
  • Journal Name: UKRAINIAN MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.612-622
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

We introduce circle plus-radical supplemented modules and strongly circle plus-radical supplemented modules (briefly, srs (aS center dot)-modules) as proper generalizations of circle plus-supplemented modules. We prove that (1) a semilocal ring R is left perfect if and only if every left R-module is an circle plus-radical supplemented module; (2) a commutative ring R is an Artinian principal ideal ring if and only if every left R-module is an srs (aS center dot)-module; (3) over a local Dedekind domain, every circle plus-radical supplemented module is an srs (aS center dot)-module. Moreover, we completely determine the structure of these modules over local Dedekind domains.