MODULES WHOSE EXACT SUBMODULES ARE ESSENTIALLY EMBEDDED IN SUMMANDS


Mutlu F. T. , TERCAN A. , YAŞAR R.

QUAESTIONES MATHEMATICAE, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.2989/16073606.2021.1982044
  • Title of Journal : QUAESTIONES MATHEMATICAE
  • Keywords: Left exact preradical, exact submodule, C-12-module, C-12(z)-module, ES-module

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.