Some hyperideals defined on the basis of the intersection of all n-ary prime hyperideals

TL;DR

This paper investigates new classes of hyperideals in Krasner (m,n)-hyperrings, based on intersections of n-ary prime hyperideals, expanding the understanding of hyperring structures.

Contribution

It introduces and explores the properties of N-hyperideals, delta-N-hyperideals, (k,n)-absorbing delta-N-hyperideals, and S-N-hyperideals in hyperring theory.

Findings

Defined new hyperideal classes in hyperrings.

Established properties and relationships among these hyperideals.

Provided major conclusions on the structure of hyperrings.

Abstract

Various classes of hyperideals have been studied in many papers in order to let us fully understand the structures of hyperrings in general. The purpose of this paper is the study of some hyperideals whose concept is created on the basis of the intersection of all n-ary prime hyperideals in category of Krasner (m,n)-hyperrings. In this regard we introduce notions of N-hyperideals, delta-N-hyperideals, (k,n)-absorbing delta-N-hyperideals and S-N-hyperideals. The overall framework of these structures in then explaind, providing a number of major conclusions.