Turkish Journal of Mathematics
DOI
10.3906/mat-1906-36
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
First Page
2327
Last Page
2336
Recommended Citation
YAŞAR, RAMAZAN
(2019)
"Modules in which semisimple fully invariant submodules are essential in summands,"
Turkish Journal of Mathematics: Vol. 43:
No.
5, Article 20.
https://doi.org/10.3906/mat-1906-36
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss5/20
