On 1-Absorbing Prime Hyperideal and Some of Its Generalizations

M. Anbarloei and Carmelo Antonio Finocchiaro

Journal of Mathematics, 2022, vol. 2022, 1-11

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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:4947019

DOI: 10.1155/2022/4947019

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