On some strongly regular relations on hyperrings

TL;DR

This paper investigates specific strongly regular relations on hyperrings, introducing new relations and concepts to derive unitary and commutative rings from hyperring structures.

Contribution

It introduces and analyzes the relations lpha^*_ and mbda^*e, and characterizes mbda_e-parts in hyperrings, advancing the understanding of hyperring relations and their associated rings.

Findings

The relation lpha^* is the transitive closure of two subrelations.

Characterization of mbda_e-parts in mbda_e-strong hyperrings.

Introduction of the relation mbda^* leading to unitary commutative rings.

Abstract

In this paper first by the fact that the relation $\alpha^*$ is the transitive closure of two its subrelations we introduce and analyze a binary relation $\lambda^*_e$ on a hyperring such that the derived ring is a unitary ring. Next we introduce and study the notion of $\lambda_e$-parts in a hyperring and we characterize $\lambda_e$-parts in a $\lambda_e$-strong hyperring $R$. Finally we introduce a new relation $\Lambda^*$ such that its derived ring be a unitary commutative ring.