O‘zbekiston matematika jurnali Volume 69 Issue 4 (2025) · pp. 46-52
On $e^*$-Semisimple Modules and the Associated Socle
Bouziri, Ayoub
Abstract
Let $R$ be a ring, and let $M$ be a right $R$-module. Recently, Baannon and Khalid introduced and studied the concept of $e^*$-essential submodules, extending the notion of essential submodules. In this context, we consider $e^*$-semisimple submodules, and we define the $e^*$-socle of $M$ as the largest $e^*$-semisimple submodule of $M$. It turns out that several properties of the socle can be extended to the $e^*$-socle. It is shown that the $e^*$-socle of $M$ is exactly the intersection of all its $e^*$-essential submodules.
$e^*$-essential submodules, $e^*$-semisimple modules, socle, $e^*$-socle
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