Modules in which semisimple fully invariant submodules are essential in summands

Authors : Ramazan Yaşar

Pages : 2327-2336

View : 14 | Download : 8

Publication Date : 9999-12-31

Article Type : Makaleler

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