Totally Goldie*-Supplemented Modules

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Güroğlu A. T.

Mathematics, vol.11, no.21, 2023 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 21
  • Publication Date: 2023
  • Doi Number: 10.3390/math11214427
  • Journal Name: Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: totally supplemented, Goldie*-supplemented module, totally Goldie*-supplemented module
  • Open Archive Collection: AVESIS Open Access Collection
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

In this paper, we first consider the properties of the Goldie*-supplemented modules, and we study the properties of totally Goldie*-supplemented modules as a version of the Goldie*-supplemented modules. A module M is called Goldie*-supplemented module if, for every submodule U of M, there exists a supplement submodule S of M such that Uβ∗S. A module M is called a totally Goldie*-supplemented module if, for every submodule A of M, A is a Goldie*-supplemented module. We emphasize that if M is totally Goldie*-supplemented, then (Formula presented.) is totally Goldie*-supplemented for some small submodule U of M. In addition, (Formula presented.) is totally Goldie*-supplemented if A and B are totally Goldie*-supplemented. Furthermore, we mention the connection between totally Goldie*-supplemented, totally supplemented, and Goldie*-supplemented.