Öz
In this paper, we introduce new expansion classes, namely weakly $ (k,n) $-absorbing hyperideals and weakly $ (k,n) $-absorbing primary hyperideals of a Krasner $ (m,n) $-hyperring, including $ (k,n) $-absorbing hyperideal and $ (k,n) $-absorbing primary hyperideal. In summary, we give generalizations of $ (k,n) $-absorbing hyperideal and $ (k,n) $-absorbing primary hyperideal. Also, we examine the relationships between classical hyperideals and the new hyperideals and explore some ways to connect them. Additionally, some main results and examples are given to explain the structures of these concepts. Finally, we study a version of Nakayama's lemma on a commutative Krasner $ (m,n) $-hyperring.
Anahtar Kelimeler
Krasner (m,n)-hyperring weakly (k,n)-absorbing hyperideals weakly (k,n)-absorbing primary hyperideals
Kaynakça
- [1] M. Al Tahan and B. Davvaz, On $(m, n)$-hyperideals in ordered semihyperrings: Applications to ordered semirings, J. Algebra Appl. 21 (5), 2250101, 2022.
- [2] R. Ameri and M.Norouzi, Prime and primary hyperideals in Krasner $(m, n)$-hyperring, European J. Combin. 34, 379-390, 2013.
- [3] R. Ameri and M. Norouzi, On multiplication $(m, n)$-hypermodules, European J. Combin. 44, 153-171, 2015.
- [4] M. Anbarloei, n-Ary 2-absorbing and n-ary 2-absorbing primary hyperideals in Krasner (m, n)-hyperrings, Mat. Vesn. 71 (3), 250-262, 2019.
- [5] M. Anbarloei, Unifing the prime and primary hyperideals under one frame in a Krasner (m, n)-hyperring, Commun. Algebra 49 (8), 3432-3446, 2021.
- [6] M. Anbarloei, J-hyperideals and their expansions in a Krasner (m, n)-hyperring, Hacet. J. Math. Stat. 52 (1), 171-184, 2023.
- [7] B. Davvaz, Fuzzy Krasner $(m, n)$-hyperrings, Comput. Math. with Appl. 59, 38793891, 2010.
- [8] B. Davvaz and V. Leoreanu-Fotea, Hyperring theory and applications, International Academic Press, USA, 2007.
- [9] K. Hila, K. Naka and B. Davvaz, On $(k, n)$-absorbing hyperideals in Krasner $(m, n)$- hyperrings, Q. J. Math. 69, 10351046, 2018.
- [10] M.Krasner, A class of hyperrings and hyperelds, Int. J. Math. Sci. 6 (2), 307-311, 1983.
- [11] S. Mirvakili and B. Davvaz, Relations on Krasner $(m, n)$-hyperrings, European J. Combin. 31, 790-802, 2010.
- [12] R.Procesi and R. Rota, On some classes of hyperstructures, Discrete Math. 208, 485-497, 1999.
- [13] A. Yassine, M.J. Nikmehr and R. Nikandish, n-Ary k-absorbing hyperideals in krasner $(m, n)$-hyperrings, Afr. Mat. 33 (1), 1-13, 2022.
Öz
Kaynakça
- [1] M. Al Tahan and B. Davvaz, On $(m, n)$-hyperideals in ordered semihyperrings: Applications to ordered semirings, J. Algebra Appl. 21 (5), 2250101, 2022.
- [2] R. Ameri and M.Norouzi, Prime and primary hyperideals in Krasner $(m, n)$-hyperring, European J. Combin. 34, 379-390, 2013.
- [3] R. Ameri and M. Norouzi, On multiplication $(m, n)$-hypermodules, European J. Combin. 44, 153-171, 2015.
- [4] M. Anbarloei, n-Ary 2-absorbing and n-ary 2-absorbing primary hyperideals in Krasner (m, n)-hyperrings, Mat. Vesn. 71 (3), 250-262, 2019.
- [5] M. Anbarloei, Unifing the prime and primary hyperideals under one frame in a Krasner (m, n)-hyperring, Commun. Algebra 49 (8), 3432-3446, 2021.
- [6] M. Anbarloei, J-hyperideals and their expansions in a Krasner (m, n)-hyperring, Hacet. J. Math. Stat. 52 (1), 171-184, 2023.
- [7] B. Davvaz, Fuzzy Krasner $(m, n)$-hyperrings, Comput. Math. with Appl. 59, 38793891, 2010.
- [8] B. Davvaz and V. Leoreanu-Fotea, Hyperring theory and applications, International Academic Press, USA, 2007.
- [9] K. Hila, K. Naka and B. Davvaz, On $(k, n)$-absorbing hyperideals in Krasner $(m, n)$- hyperrings, Q. J. Math. 69, 10351046, 2018.
- [10] M.Krasner, A class of hyperrings and hyperelds, Int. J. Math. Sci. 6 (2), 307-311, 1983.
- [11] S. Mirvakili and B. Davvaz, Relations on Krasner $(m, n)$-hyperrings, European J. Combin. 31, 790-802, 2010.
- [12] R.Procesi and R. Rota, On some classes of hyperstructures, Discrete Math. 208, 485-497, 1999.
- [13] A. Yassine, M.J. Nikmehr and R. Nikandish, n-Ary k-absorbing hyperideals in krasner $(m, n)$-hyperrings, Afr. Mat. 33 (1), 1-13, 2022.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Ekim 2023 |
| Yayımlandığı Sayı | Yıl 2023 Cilt: 52 Sayı: 5 |