Merging N-hyperideals and J-hyperideals in one frame

TL;DR

This paper introduces a unified framework called n-ary delta(0)-hyperideals that combines N-hyperideals and J-hyperideals in Krasner (m,n)-hyperrings, providing new characterizations and properties.

Contribution

It merges N-hyperideals and J-hyperideals into a single concept of n-ary delta(0)-hyperideals and explores their properties and applications in hyperring theory.

Findings

Characterization of n-ary delta(0)-hyperideals

Properties of hyperintegral domains and local hyperrings

Introduction of (s,n)-absorbing delta(0)-hyperideals

Abstract

The notions of N-hyperideals and J-hyperideals as two classes of hyperideals were recently defined in the context of Krasner (m,n)-hyperrings. These concepts are created on the basis of the intersection of all n-ary prime hyperideals and the intersection of all maximal hyperideals, respectively. Despite being vastly different in many aspects, they shar numerous similar properties. The aim of this research work is to merge them under one frame called n-ary delta(0)-hyperideals where the function delta assigns to each hyperideals of a Krasner (m,n)-hyperring a hyperideal of the same hyperring. We give various properties of n-ary delta(0)-hyperideals and use them to characerize certain classes of hyperring such as hyperintegral domains and local hyperrings. Moreover, we introduce the notions of (s,n)-absorbing delta(0)-hyperideals and weakly (s,n)-absorbing delta(0)-hyperideals.