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Turkish Journal of Mathematics

RAMAZAN YAŞAR

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.

DOI

10.3906/mat-1906-36

Keywords

Extending module, socle of a module, $C_{11}$-module, Weak $CS$-module, fully invariant, $FI$-extending

First Page

2327

Last Page

2336

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