Modules in which semisimple fully invariant submodules are essential in summands


YAŞAR R.

TURKISH JOURNAL OF MATHEMATICS, vol.43, no.5, pp.2327-2336, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 5
  • Publication Date: 2019
  • Doi Number: 10.3906/mat-1906-36
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.2327-2336

Abstract

One of the useful generalization of extending notion is FI-extending property. A module is called FI-extending if every fully invariant submodule is essential in a direct summand. In this paper, we explore Weak FI-extending concept by considering only semisimple fully invariant submodules rather than all fully invariant submodules. To this end, we call such a module Weak FI-extending. We obtain that FI-extending modules are properly contained in this new class of modules. Amongst other structural properties, we also deal with direct sums and direct summands of Weak FI-extending modules.