ON THE TOPOLOGICAL STRUCTURES ON Γ-SEMIRINGS

Abstract

In this paper, we introduce some special classes of ideals in Γ-semirings called prime k-ideal, prime full k-ideal, prime ideals, maximal and strongly irreducible ideals. Considering and investigating properties of the collection A , T , M , B and S of all proper prime k-ideals, proper prime full k-ideals, maximal ideals, prime ideals and strongly irreducible ideals, respectively, of a Γ- semiring R, we construct the respective topologies on them by means of closure operator defined in terms of intersection and inclusion relation among these ideals of Γ-semiring R. The respective obtained topological spaces are called the structure spaces of the Γ-semiring R. We study a several principal topological axioms and properties in those structure spaces of Γ-semiring such as separation axioms, compactness and connectedness etc.