Primitive hyperideals and hyperstructure spaces of hyperrings

TL;DR

This paper introduces primitive hyperideals in hyperrings, explores their relations with other hyperideals, and studies the topological structure of the space of primitive hyperideals using Jacobson topology.

Contribution

It defines primitive hyperideals in hyperrings and establishes their topological and algebraic properties, connecting them with maximal and prime hyperideals for the first time.

Findings

Defined primitive hyperideals in hyperrings.

Established Jacobson topology on the set of primitive hyperideals.

Analyzed topological properties of the hyperstructure space.

Abstract

We introduce primitive hyperideals of a hyperring R and show relations with R itself, and with maximal and prime hyperideals of R. We endow a Jacobson topology on the set of primitive hyperideals of R and study topological properties of the corresponding hyperstructure space.