t-Generalized Supplemented Modules

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Kosar B., Nebiyev C.

UKRAINIAN MATHEMATICAL JOURNAL, vol.67, no.11, pp.1678-1686, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 67 Issue: 11
  • Publication Date: 2016
  • Doi Number: 10.1007/s11253-016-1182-9
  • Journal Name: UKRAINIAN MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1678-1686
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In the present paper, t-generalized supplemented modules are defined starting from the generalized a-supplemented modules. In addition, we present examples separating the t-generalized supplemented modules, supplemented modules, and generalized a-supplemented modules and also show the equality of these modules for projective and finitely generated modules. Moreover, we define cofinitely t-generalized supplemented modules and give the characterization of these modules. Furthermore, for any ring R, we show that any finite direct sum of t-generalized supplemented R-modules is t-generalized supplemented and that any direct sum of cofinitely t-generalized supplemented R-modules is a cofinitely t-generalized supplemented module.