Module Decompositions by Images of Fully Invariant Submodules

Creative Commons License

Calci T., ÜNGÖR B., Harmanci A.

Filomat, vol.35, no.11, pp.3679-3687, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 11
  • Publication Date: 2021
  • Doi Number: 10.2298/fil2111679p
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.3679-3687
  • Keywords: Dual Rickart module, image split module, fully invariant submodule, direct summand
  • Ankara University Affiliated: Yes

Abstract

Let R be a ring with identity, M be a right R-module and F be a fully invariant submodule of M. The concept of an F-inverse split module M has been investigated recently. In this paper, we approach to this concept with a different perspective, that is, we deal with a notion of an F-image split module M, and study various properties and obtain some characterizations of this kind of modules. By means of F-image split modules M, we focus on modules M in which fully invariant submodules F are dual Rickart direct summands. In this way, we contribute to the notion of a T-dual Rickart module M by considering Z2 (M) as the fully invariant submodule F of M. We also deal with a notion of relatively image splitness to investigate direct sums of image split modules. Some applications of image split modules to rings are given.