ON STRONGLY circle plus-SUPPLEMENTED MODULES

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Nebiyev C., Pancar A.

UKRAINIAN MATHEMATICAL JOURNAL, vol.63, no.5, pp.768-775, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 63 Issue: 5
  • Publication Date: 2011
  • Doi Number: 10.1007/s11253-011-0541-9
  • Journal Name: UKRAINIAN MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.768-775
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

Strongly circle plus-supplemented and strongly cofinitely circle plus-supplemented modules are defined and some properties of strongly circle plus-supplemented and strongly cofinitely circle plus-supplemented modules are investigated. Let R be a ring. Then every R-module is strongly circle plus-supplemented if and only if R is perfect. The finite direct sum of circle plus-supplemented modules is circle plus-supplemented. However, this is not true for strongly circle plus-supplemented modules. Any direct sum of cofinitely circle plus-supplemented modules is cofinitely circle plus-supplemented but this is not true for strongly cofinitely circle plus-supplemented modules. We also prove that a supplemented module is strongly circle plus-supplemented if and only if every supplement submodule lies above a direct summand.