آمار
| تعداد نشریات | 26 |
| تعداد شماره‌ها | 447 |
| تعداد مقالات | 4,557 |
| تعداد مشاهده مقاله | 5,380,001 |
| تعداد دریافت فایل اصل مقاله | 3,580,066 |
Weakly $S$-prime hyperideals | ||
| Journal of Mahani Mathematical Research | ||
| دوره 14، شماره 2 - شماره پیاپی 32، مرداد 2025، صفحه 175-190 اصل مقاله (504.63 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2025.23922.1689 | ||
| نویسنده | ||
| Mahdi Anbarloei* | ||
| Department of Mathematics, Faculty of Sciences, Imam Khomeini, International University, Qazvin, Iran | ||
| چکیده | ||
| The purpose of this paper is presenting a new expansion class, namely weakly $n$-ary $S$-prime hyperideals in Krasner $(m,n)$-hyperrings. In summary, we give an extension of $n$-ary $S$-prime hyperideals. Some results and examples are given to explain the structure of this new concept. Moreover, a version of Nakayama$^,$s Lemma is considered on commutative Krasner $(m,n)$-hyperrings. | ||
| کلیدواژه‌ها | ||
| $n$-ary multiplicative set؛ weakly $n$-ary $S$-prime hyperideal؛ strongly weakly $n$-ary $S$-prime hyperideal | ||
| مراجع | ||
|
[1] Almahdi, F. A., Bouba, E. M., & Tamekkante, M. (2021). On weakly S-prime ideals of commutative rings. An. Stiint. Univ. Ovidius Constanta Ser. Mat., 29(2), 173-186.
[2] Ameri, R., & Norouzi, M. (2013). Prime and primary hyperideals in Krasner (m; n)-hyperrings. European Journal of Combinatorics, 34, 379-390.
[3] Anbarloei, M. (2023). Krasner (m; n)-hyperring of fractions. Jordan Journal of Mathematics and Statistic, 16(1), 165-185.
[4] Anbarloei, M. (2023). Extension of n-ary prime hyperideals via an n-ary multiplicative subset in a Krasner (m; n)-hyperring. Filomat, 37(12), 3857-3869.
[5] Anvariyeh, S. M., Mirvakili, S., & Davvaz, B. (2010). Fundamental relation on (m; n)-hypermodules over (m; n)-hyperrings. Ars Combin., 94, 273-288.
[6] Corsini, S. (1993). Prolegomena of hypergroup theory (2nd ed.). Aviani editor, Italy.
[7] Davvaz, B., & Leoreanu-Fotea, V. (2007). Hyperring Theory and Applications. International Academic Press, Palm Harbor, USA.
[8] Davvaz, B., Ulucak, G., & Tekir, U. (2023). Weakly (k; n)-absorbing (Primary) hyper-ideals of a Krasner (m; n)-hyperring. Hacet. J. Math. Stat., 52(5), 1229-1238.
[9] Davvaz, B., Goswami, A., & Howell, K. T. (2024). Primitive hyperideals and hyperstructure spaces of hyperrings. Categ. Gen. Algebr. Struct. Appl., In press.
[10] Hamed, A., & Malek, A. (2019). S-prime ideals of a commutative ring. Beitr Algebra Geom. https://doi.org/10.1007/s13366-019-00476-5
[11] Hila, K., Naka, K., & Davvaz, B. (2018). On (k; n)-absorbing hyperideals in Krasner (m; n)-hyperrings. Quarterly Journal of Mathematics, 69, 1035-1046.
[12] Marty, F. (1934). Sur une generalization de la notion de groupe. 8th Congress Math., Scandenaves, Stockholm, 45-49.
[13] Mirvakili, S., & Davvaz, B. (2010). Relations on Krasner (m; n)-hyperrings. European J. Combin., 31, 790-802.
[14] Mirvakili, S., & Davvaz, B. (2015). Constructions of (m; n)-hyperrings. Matematicki Vesnik, 67(1), 1-16.
[15] Norouzi, M., Ameri, R., & Leoreanu-Fotea, V. (2018). Normal hyperideals in Krasner (m; n)-hyperrings. An. St. Univ. Ovidius Constanta, 26(3), 197-211.
[16] Ostadhadi-Dehkordi, S., & Davvaz, B. (2016). A Note on Isomorphism Theorems of Krasner (m; n)- hyperrings. Arabian Journal of Mathematics, 5, 103-115.
[17] Sharp, R. Y. (2000). Steps in Commutative Algebra (2nd ed.). Cambridge University Press, Cambridge.
[18] Vougiouklis, T. (1994). Hyperstructures and their representations. Hadronic Press Inc., Florida. | ||
|
آمار تعداد مشاهده مقاله: 105 تعداد دریافت فایل اصل مقاله: 101 |
||