Classes of F-hyperideals of a Krasner F^{(m,n)}-hyperring

TL;DR

This paper introduces and characterizes three new classes of F-hyperideals—prime, maximal, and primary—in Krasner F^{(m,n)}-hyperrings, expanding the algebraic structure theory of hyperrings.

Contribution

It defines and characterizes prime, maximal, and primary F-hyperideals within Krasner F^{(m,n)}-hyperrings, a novel extension in hyperring theory.

Findings

Defined prime, maximal, and primary F-hyperideals.

Provided characterizations for each class.

Extended the algebraic framework of Krasner F^{(m,n)}-hyperrings.

Abstract

Krasner F^{(m,n)}-hyperring were introduced and investigated by Farshi and Davvaz. In this paper, our purpose is to define and characterize three classes of F-hyperideals in a Krasner F^{(m,n)}-hyperring, namely, prime F-hyperideals, maximal F-hyperideals and primary F-hyperideals.