On 1-Absorbing Prime Hyperideal and Some of Its Generalizations
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 multip...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/4947019 |
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| author | M. Anbarloei |
| author_facet | M. Anbarloei |
| author_sort | M. Anbarloei |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-94ae722cf43346e69c963b0c40a5395c |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-94ae722cf43346e69c963b0c40a5395c2025-02-03T05:51:01ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/4947019On 1-Absorbing Prime Hyperideal and Some of Its GeneralizationsM. Anbarloei0Department of MathematicsIn 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.http://dx.doi.org/10.1155/2022/4947019 |
| spellingShingle | M. Anbarloei On 1-Absorbing Prime Hyperideal and Some of Its Generalizations Journal of Mathematics |
| title | On 1-Absorbing Prime Hyperideal and Some of Its Generalizations |
| title_full | On 1-Absorbing Prime Hyperideal and Some of Its Generalizations |
| title_fullStr | On 1-Absorbing Prime Hyperideal and Some of Its Generalizations |
| title_full_unstemmed | On 1-Absorbing Prime Hyperideal and Some of Its Generalizations |
| title_short | On 1-Absorbing Prime Hyperideal and Some of Its Generalizations |
| title_sort | on 1 absorbing prime hyperideal and some of its generalizations |
| url | http://dx.doi.org/10.1155/2022/4947019 |
| work_keys_str_mv | AT manbarloei on1absorbingprimehyperidealandsomeofitsgeneralizations |