Complemented and completely regular $\Gamma-$ semirings

Document Type : Research Paper

Authors

1 Himachal Pradesh University Regional Centre‎, ‎Dharamshala (H.P.)‎, ‎India

2 Government Degree College‎, ‎Dharamshala(H.P.), India

Abstract

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.

Keywords

Main Subjects

References

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Journal of Algebra and Related Topics
Volume 14, Issue 1
August 2026
Pages 115-126

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