$k$-Congruences and the Zariski topology in semirings

Year 2021, Volume: 50 Issue: 3, 699 - 709, 07.06.2021

Song-chol Han

https://doi.org/10.15672/hujms.614688

Cited By: 3

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

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