A GENERALIZATION OF PRIME HYPERIDEALS | ||
| Journal of Algebraic Systems | ||
| مقاله 11، دوره 8، شماره 1، آذر 2020، صفحه 113-127 اصل مقاله (182.83 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2019.8491.1412 | ||
| نویسنده | ||
| M. Anbarloei* | ||
| Department of Mathematics, Faculty of Sciences, Imam Khomeini International University, Qazvin, Iran. | ||
| چکیده | ||
| Let $R$ be a multiplicative hyperring. In this paper, we introduce and study the concept of n-absorbing hyperideal which is a generalization of prime hyperideal. A proper hyperideal $I$ of $R$ is called an $n$-absorbing hyperideal of $R$ if whenever $\alpha_1o...o\alpha_{n+1} \subseteq I$ for $\alpha_1,...,\alpha_{n+1} \in R$, then there are $n$ of the $\alpha_i^,$s whose product is in $I$. | ||
| کلیدواژهها | ||
| prime hyperideal؛ n-absorbing hyperideal؛ primary hyperideal؛ hyperring | ||
| مراجع | ||
|
1. R. Ameri, A. Kordi and S. Hoskova-Mayerova, Multiplicative hyperring of fractions and coprime hyperideals, An. St. Univ. Ovidius Constanta, 25 (2017), 5–23. 2. M. Anbarloei, On 2-absorbing and 2-absorbing primary hyperideals of a multiplicative hyperring, Cogent Math., (2017), Article ID: 1354447, 8 pp. 3. A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc., 75 (2007), 417–429. 4. A. Badawi and D. F. Anderson, On n-absorbing ideals of commutative rings, Comm. Algebra, 39 (5) (2011), 1646-1672. 5. S. Corsini, Prolegomena of hypergroup theory, Second edition, Aviani editor, Italy, 1993. 6. S. Corsini and V. Leoreanu, Applications of hyperstructure theory, Advances in Mathematics, Vol. 5, Kluwer Academic Publishers, 2003. 7. U. Dasgupta, On prime and primary hyperideals of a multiplicative hyperrings, An. Stint. Univ. Al. I. Cuza Iasi, 58 (2012), 19–36. 8. U. Dasgupta, On certain classes of hypersemirings, PhD Thsis, University of Calcutta, 2012. 9. B. Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, Palm Harbor, USA, 2007. 10. P. Ghiasvand, On 2-absorbing hyperideals of multiplicative hyperrings, Second Seminar on Algebra and its Applications, (2014), 58–59. 11. K. Hila and B. Davvaz, On (k; n)-absorbing hyperideals in Krasner (m; n)- hyperrings, Q. J. Math., 69 (2018), 1035–1046. 12. L. Kamali Ardakani and B. Davvaz, A generalization of prime hyperideals in krasner hyperrings, J. Algebraic Systems, 7 (2020), 205–216. 13. F. Marty, Sur une generalization de la notion de groupe, 8th Congres Math. Scandenaves, Stockholm, (1934), 45–49. 14. J. Mittas, Hypergroupes canoniques, Math. Balkanica, 2 (1972), 165–179. 15. S. Omidi and B. Davvaz, Contribution to study special kinds of hyperideals in ordered semihyperrings, J. Taibah Univ. Sci., 11 (2017), 1083–1094. 16. R. Rota, Sugli iperanelli moltiplicativi, Rend. Di Math., Series VII, 4 (1982), 711–724. 17. E. Sevim, B. A. Ersoy and B. Davvaz, Primary hyperideals of multiplicative hyperrings, Int. Balkan J. Math., 1 (2018), 43–49. 18. G. Ulucak, On expansions of prime and 2-absorbing hyperideals in multiplicative hyperrings, Turkish J. Math., 43 (2019), 1504–1517. 19. T. Vougiouklis, Hyperstructures and their representations, Hadronic Press Inc., Florida, 1994. 20. T. Vougiouklis, The fundamental relation in hyperrings. The general hyperfield, In: Proceedings of fourth international congress on algebraic hyperstructures and applications (AHA 1990), World Scientific, 1991. | ||
|
آمار تعداد مشاهده مقاله: 950 تعداد دریافت فایل اصل مقاله: 812 |
||