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On 1‐Absorbing Prime Hyperideal and Some of Its Generalizations

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  • M. Anbarloei

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.

Suggested Citation

  • M. Anbarloei, 2022. "On 1‐Absorbing Prime Hyperideal and Some of Its Generalizations," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:4947019
    DOI: 10.1155/2022/4947019
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    References listed on IDEAS

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    1. Marc Krasner, 1983. "A class of hyperrings and hyperfields," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 6, pages 1-5, January.
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