SOME STRUCTURE SPACES OF GENERALIZED SEMIRINGS

Abstract

In this paper, we study some structure spaces of (m; n)-semiring
(S; f; g), introducing the classes of n-ary prime k-ideals, n-ary prime full k-
ideals, n-ary prime ideals, maximal ideals and strongly irreducible ideals.
Considering their collections, respectively, of an (m; n)-semiring (S; f; g), we
construct the respective topologies on them by means of closure operator de-
ned in terms of intersection and inclusion relation among these ideals of the
(m; n)-semiring (S; f; g). The obtained topological spaces are called the structure
spaces of (m; n)-semiring (S; f; g). We mainly study several principal
topological axioms and properties of those structure spaces of (m; n)-semiring
such as separation axioms, compactness and connectedness etc.