O‘zbekiston matematika jurnali 69-том 4-нөмір (2025) · 46-52-беттер

On $e^*$-Semisimple Modules and the Associated Socle

Bouziri, Ayoub

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Аңдатпа

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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APA 7 
Bouziri, Ayoub (2025). On $e^*$-Semisimple Modules and the Associated Socle. O‘zbekiston matematika jurnali, 69(4), 46-52.
GOST R 7.0.5 
Bouziri, Ayoub On $e^*$-Semisimple Modules and the Associated Socle // O‘zbekiston matematika jurnali. 2025. Т. 69. № 4. С. 46-52.
BibTeX 
@article{ayoub2025,
  author  = {Bouziri, Ayoub},
  title   = {On $e^*$-Semisimple Modules and the Associated Socle},
  journal = {O‘zbekiston matematika jurnali},
  year    = {2025},
  volume  = {69},
  number  = {4},
  pages   = {46-52}
}
RIS 
TY  - JOUR
AU  - Bouziri, Ayoub
TI  - On $e^*$-Semisimple Modules and the Associated Socle
JO  - O‘zbekiston matematika jurnali
PY  - 2025
VL  - 69
IS  - 4
SP  - 46
EP  - 52
ER  -