Some structure spaces of generalized semirings

Abstract

In this paper, we study some structure spaces of (m, n)-semiring (S, f,), 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,), we construct the respective topologies on them by means of closure operator defined in terms of intersection and inclusion relation among these ideals of the (m, n)-semiring (S, f,). The obtained topological spaces are called the structure spaces of (m, n)-semiring (S, f,). 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.

Structures of (m,n)-seminearring

“…Konsep (𝑚, 𝑛)-semiring telah diperkenalkan dan beberapa sifatsifatnya telah didiskusikan dalam artikel: Pop & Pop (2008; Alam, dkk. (2013); Hila (2018); Pop & Lauran (2018); Davvaz & Mohammadi (2021); Chaudhari, dkk. (2021).…”