Complemented and completely regular \Gamma- semirings

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+۱ = x\alpha y for all x,y \in R‎, ‎\alpha \in \Gamma and prove that R is a partially ordered \Gamma- semiring.

کلیدواژه ها:

Regular band‎ ، ‎\Gamma-semigroup‎ ، Quasi-separative‎ ، Partially ordered \Gamma- semiring