On 1-absorbing prime hyperideal and some of its generalizations

TL;DR

This paper introduces and explores the concept of 1-absorbing prime hyperideals in multiplicative hyperrings, generalizing prime hyperideals, and investigates related notions like primary and strongly primary hyperideals.

Contribution

It defines new classes of hyperideals in hyperrings and studies their properties, extending the theory of prime hyperideals in algebraic structures.

Findings

Properties of 1-absorbing prime hyperideals established

Introduction of 1-absorbing primary and related hyperideals

Generalizations extend the understanding of hyperideal structures

Abstract

Let R be a multiplicative hyperring. In this paper, we define the concept of 1-absorbing prime hyperideals which is a generalization of the prime hyperideals. Several properties of the hyperideals are provided. Moreover, we introduce the notions of 1-absorbing primary hyperideals, strongly 1-absorbing primary hyperideals and weakly 1-absorbing primary hyperideals which are generalizations of the 1-absorbing prime hyperideals and then we will show some properties of them.