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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We then obtained some results for these newly defined semigroups.
📌 3 Key Takeaways
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Objective & Hypothesis:Let $S$ be a $\Gamma$-semigroup with zero.
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Key Findings & Data: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 $S$.
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Conclusion & Impact:We then obtained some results for these newly defined semigroups.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Source of $\Gamma$-semiprimeness · $\lvert S_{S}^{\Gamma}\rvert$-idempotent $\Gamma$-semigroup · $\lvert S_{S}^{\Gamma}\rvert$-regular $\Gamma$-semigroup
Abstract
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.
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Cite This Article
Yeşil, D., Mekera, R., Camcı, D. K. (2025). The Source of $\Gamma$-semiprimeness on $\Gamma$-semigroups. Turkish Journal of Mathematics and Computer Science, Volume: 17 Issue: 1. https://doi.org/10.47000/tjmcs.1378193