On 1-Absorbing Prime Hyperideal and Some of Its Generalizations

Abstract

In this paper, we introduce the concept of 1-absorbing prime hyperideals which is an expansion of the prime hyperideals. Several properties of the hyperideals are provided. For example, it is proved that if a strong C-hyperideal $I$ of $R$ is 1-absorbing prime that is not prime, then $R$ is a local multiplicative hyperring. Moreover, we introduce and study 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. We also examine the relations between these new concepts and other hyperideals.