Zariski topology of (Krasner) hyperrings

TL;DR

This paper explores the Zariski topology on Krasner hyperrings, analyzing the prime spectrum, topological properties, and their connections to algebraic structures, advancing the understanding of hyperring geometry.

Contribution

It introduces a topology on strongly regular relations and studies the influence of fundamental relations on the Zariski topology of Krasner hyperrings.

Findings

Prime spectrum of Krasner hyperrings studied

Relationship between topological and algebraic properties established

Topology on strongly regular relations defined and analyzed

Abstract

In this article, we will study prime spectrum of Krasner hyperrings and Zariski topology on them, which play an important role in algebraic geometry. Then some results about the relationship between the topological properties of Spec(R) and the algebraic properties of the hyperring R will be proved. In the following, by proving that every strongly regular relation on Krasner hyperrings can be considered as a congruence relation, we will define a topology on the set of strongly regular relations, and investigate its relationship with the Zariski topology. In addition, the effect of fundamental relations on the Zariski topology of Krasner hyperrings will also be investigated.