Remarks on J-hyperideals and their expansion

TL;DR

This paper introduces and characterizes new classes of hyperideals in Krasner (m,n)-hyperrings, including n-ary J-hyperideals and their expansions, extending the theory of hyperideals in algebraic structures.

Contribution

It defines and explores n-ary J-hyperideals, delta-J-hyperideals, and (k,n)-absorbing delta-J-hyperideals, expanding the framework of hyperideal theory in hyperrings.

Findings

Defined n-ary J-hyperideals in Krasner (m,n)-hyperrings

Characterized properties of delta-J-hyperideals and their extensions

Extended the concept to (k,n)-absorbing delta-J-hyperideals

Abstract

The aim of this research work is to define and characterize a new class of hyperideals in a Krasner (m,n)-hyperring that we call n-ary J-hyperideals. Also, we study the concept of n-ary delta-J-hyperideals as an expansion of n-ary J-hyperideals. Finally, we extend the notion of n-ary delta-J-hyperideals to (k,n)-absorbing delta-J-hyperideals.