University of Guilan Journal of Algebra and Related Topics 2345-3931 Articles in Press 2025 12 27 Complemented and completely regular $\Gamma-$ semirings 9320 10.22124/jart.2025.29305.1747 EN T. R. Sharma Himachal Pradesh University Regional Centre‎, ‎Dharamshala (H.P.)‎, ‎India R. Kumar Government Degree College‎, ‎Dharamshala(H.P.), India Journal Article 2024 12 20 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. https://jart.guilan.ac.ir/article_9320_ee554eb1d4f02e9413021fcc2e6d05eb.pdf