$k$-Congruences and the Zariski topology in semirings

Authors : Songchol HAN

Pages : 699-709

Doi:10.15672/hujms.614688

View : 22 | Download : 8

Publication Date : 2021-06-07

Article Type : Research Paper

Abstract :The purpose of this paper is to study topological properties of both the set of all $k$-prime ideals and the set of all $k$-prime congruences for any commutative semiring with zero and identity. We first prove that the $k$-prime spectrum, i.e. the set of all $k$-prime ideals equipped with the Zariski topology is a spectral space, and then prove that the set of all $k$-prime congruences is homeomorphic to the $k$-prime spectrum with respect to their Zariski topologies.
Keywords : semiring, ideal, congruence, prime ideal, Zariski topology