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.
Sharma, T. R. and Kumar, R. (2025). Complemented and completely regular $\Gamma-$ semirings. Journal of Algebra and Related Topics, (), -. doi: 10.22124/jart.2025.29305.1747
MLA
Sharma, T. R., and Kumar, R. . "Complemented and completely regular $\Gamma-$ semirings", Journal of Algebra and Related Topics, , , 2025, -. doi: 10.22124/jart.2025.29305.1747
HARVARD
Sharma, T. R., Kumar, R. (2025). 'Complemented and completely regular $\Gamma-$ semirings', Journal of Algebra and Related Topics, (), pp. -. doi: 10.22124/jart.2025.29305.1747
CHICAGO
T. R. Sharma and R. Kumar, "Complemented and completely regular $\Gamma-$ semirings," Journal of Algebra and Related Topics, (2025): -, doi: 10.22124/jart.2025.29305.1747
VANCOUVER
Sharma, T. R., Kumar, R. Complemented and completely regular $\Gamma-$ semirings. Journal of Algebra and Related Topics, 2025; (): -. doi: 10.22124/jart.2025.29305.1747
)