Modules whose exact submodules are essentially embedded in summands

Takıl Mutlu F., TERCAN A., YAŞAR R.

Quaestiones Mathematicae, vol.45, no.12, pp.1977-1986, 2022 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 12
  • Publication Date: 2022
  • Doi Number: 10.2989/16073606.2021.1982044
  • Journal Name: Quaestiones Mathematicae
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.1977-1986
  • Keywords: -module, C12-module, ES-module, exact submodule, Left exact preradical
  • Ankara University Affiliated: No

Abstract

In this article we study the condition that every exact submodule is essentially embedded in direct summands in a module. It is shown that the class of modules with former property is closed under direct sums. However, we provide examples which show that this new class of modules is not closed under direct summands. Failure of the latter closure property allows us to establish results on the inheritance of our condition by direct summands.