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Complemented and completely regular $\Gamma-$ semirings | ||
| Journal of Algebra and Related Topics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 06 دی 1404 | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2025.29305.1747 | ||
| نویسندگان | ||
| T. R. Sharma* 1؛ R. Kumar2 | ||
| 1Himachal Pradesh University Regional Centre, Dharamshala (H.P.), India | ||
| 2Government Degree College, Dharamshala(H.P.), India | ||
| چکیده | ||
| This paper investigates the additive and multiplicative properties of complemented and completely regular $\Gamma-$ semirings. We prove many results on different structures of $\Gamma-$ semirings like anti-inverse, quasi-separative, distributive, and partial order. Boolean $\Gamma-$ semiring is demonstrated by applying the concept of a completely regular $\Gamma-$ semiring. Finally, by using the idea of simple and completely regular $\Gamma-$ semiring, we define a relation $\leq$ on $R$ such that $x \leq y$ if and only if $x+y+1 = x\alpha y$ for all $x,y \in R, \alpha \in \Gamma $ and prove that $R$ is a partially ordered $\Gamma-$ semiring. | ||
| کلیدواژهها | ||
| Regular band؛ $\Gamma-$semigroup؛ Quasi-separative؛ Partially ordered $\Gamma-$ semiring | ||
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آمار تعداد مشاهده مقاله: 3 |
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