TY  - JOUR
T1  - The Source of $\Gamma$-semiprimeness on $\Gamma$-semigroups
AU  - Mekera, Rasie
AU  - Yeşil, Didem
AU  - Karalarlıoğlu Camcı, Didem
PY  - 2025
DA  - June
Y2  - 2025
DO  - 10.47000/tjmcs.1378193
JF  - Turkish Journal of Mathematics and Computer Science
JO  - TJMCS
PB  - Matematikçiler Derneği
WT  - DergiPark
SN  - 2148-1830
SP  - 10
EP  - 16
VL  - 17
IS  - 1
LA  - en
AB  - Let $S$ be a $\Gamma$-semigroup with zero. We define the $S_{S}^{\Gamma}$ subset of $S$ as $S_{S}^{\Gamma}=\{a\in S \mid a\Gamma (S\Gamma a)=(0)\}.$ This set is called the source of $\Gamma$-semiprimeness of $S$. In this study, we examined some properties of $S_{S}^{\Gamma}$ set and defined $\lvert S_{S}^{\Gamma}\rvert$-idempotent , $\lvert S_{S}^{\Gamma}\rvert$-regular and $\lvert S_{S}^{\Gamma}\rvert$-reduced $\Gamma$-semigroups. We then obtained some results for these newly defined semigroups.
KW  - Source of $\Gamma$-semiprimeness
KW  - $\lvert S_{S}^{\Gamma}\rvert$-idempotent $\Gamma$-semigroup
KW  - $\lvert S_{S}^{\Gamma}\rvert$-regular $\Gamma$-semigroup
KW  - $\lvert S_{S}^{\Gamma}\rvert$-reduced $\Gamma$-semigroup
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UR  - https://doi.org/10.47000/tjmcs.1378193
L1  - https://dergipark.org.tr/en/download/article-file/3484183
ER  -