On Properties of Generalized Bi-{\Gamma}-Ideals of {\Gamma}-Semirings

TL;DR

This paper explores the properties of generalized bi-{\Gamma}-ideals within the framework of {\Gamma}-semirings, expanding the theoretical understanding of these algebraic structures.

Contribution

It introduces and investigates the properties of generalized bi-{\Gamma}-ideals in {\Gamma}-semirings, extending previous work in the area.

Findings

Characterization of generalized bi-{\Gamma}-ideals

Relationships between different types of ideals in {\Gamma}-semirings

Conditions under which generalized bi-{\Gamma}-ideals exhibit specific properties

Abstract

The notion of $\Gamma$-semirings was introduced by Murali Krishna Rao \cite{Rao} as a generalization of the notion of $\Gamma$-rings as well as of semirings. We have known that the notion of $\Gamma$-semirings is a generalization of the notion of semirings. In this paper, extending Kaushik, Moin and Khan's work, we generalize the notion of generalized bi-$\Gamma$-ideals of $\Gamma$-semirings and investigate some related properties of generalized bi-$\Gamma$-ideals.