Extensions of $n$-ary prime hyperideals via an $n$-ary multiplicative subset in a Krasner $(m,n)$-hyperring

TL;DR

This paper introduces n-ary S-prime hyperideals in Krasner (m,n)-hyperrings, explores their properties, stability, and extends the concept to n-ary S-primary hyperideals, enriching hyperring theory.

Contribution

It defines and studies n-ary S-prime hyperideals and extends the concept to S-primary hyperideals within Krasner (m,n)-hyperrings, providing new theoretical insights.

Findings

Characterization of n-ary S-prime hyperideals

Stability results under hyperring constructions

Extension to n-ary S-primary hyperideals

Abstract

Let R be a Krasner (m,n)-hyperring and S be an n-ary multiplicative subset of R. The purpose of this paper is to introduce the notion of n-ary S-prime hyperideals as a new expansion of n-ary prime hyperideals. Several properties and characterizations concerning n-ary S-prime hyperideals are presented. The stability of this new concept with respect to various hyperring-theoretic constructions are studied. Furthermore, we extend this concept to n-ary S-primary hyperideals. We obtained some specific results explaining the structure.