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Totally Goldie*-Supplemented Modules

Author

Listed:
  • Ayşe Tuğba Güroğlu

    (Department of Mathematics, Faculty of Arts and Sciences, Manisa Celal Bayar University, Manisa 45140, Turkey)

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 M U is totally Goldie*-supplemented for some small submodule U of M . In addition, M = A ⊕ B 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.

Suggested Citation

  • Ayşe Tuğba Güroğlu, 2023. "Totally Goldie*-Supplemented Modules," Mathematics, MDPI, vol. 11(21), pages 1-8, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4427-:d:1267362
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