MODULES WHOSE EXACT SUBMODULES ARE ESSENTIALLY EMBEDDED IN SUMMANDS

Mutlu F. T., TERCAN A., YAŞAR R.

QUAESTIONES MATHEMATICAE, vol.45, no.12, pp.1977-1986, 2022 (SCI-Expanded) identifier 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: Left exact preradical, exact submodule, C-12-module, C-12(z)-module, ES-module
  • Hacettepe University Affiliated: Yes

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.