Weakly $ (k,n) $-absorbing (primary) hyperideals of a Krasner $ (m,n) $-hyperring

Bijan Davvaz; Gülşen Ulucak; Ünsal Tekir

doi:10.15672/hujms.1199437

Research Article

Weakly $ (k,n) $-absorbing (primary) hyperideals of a Krasner $ (m,n) $-hyperring

Year 2023, Volume: 52 Issue: 5, 1229 - 1238, 31.10.2023

Bijan Davvaz Gülşen Ulucak Ünsal Tekir

https://doi.org/10.15672/hujms.1199437

Abstract

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.

Keywords

Krasner (m,n)-hyperring, weakly (k,n)-absorbing hyperideals, weakly (k,n)-absorbing primary hyperideals

References

[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.

Year 2023, Volume: 52 Issue: 5, 1229 - 1238, 31.10.2023

Bijan Davvaz Gülşen Ulucak Ünsal Tekir

https://doi.org/10.15672/hujms.1199437

Abstract

References

[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.

There are 13 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Mathematics
Authors	Bijan Davvaz 0000-0003-1941-5372 Gülşen Ulucak 0000-0001-6690-6671 Ünsal Tekir 0000-0003-0739-1449
Publication Date	October 31, 2023
Published in Issue	Year 2023 Volume: 52 Issue: 5

Cite

APA	Davvaz, B., Ulucak, G., & Tekir, Ü. (2023). Weakly $ (k,n) $-absorbing (primary) hyperideals of a Krasner $ (m,n) $-hyperring. Hacettepe Journal of Mathematics and Statistics, 52(5), 1229-1238. https://doi.org/10.15672/hujms.1199437
AMA	Davvaz B, Ulucak G, Tekir Ü. Weakly $ (k,n) $-absorbing (primary) hyperideals of a Krasner $ (m,n) $-hyperring. Hacettepe Journal of Mathematics and Statistics. October 2023;52(5):1229-1238. doi:10.15672/hujms.1199437
Chicago	Davvaz, Bijan, Gülşen Ulucak, and Ünsal Tekir. “Weakly $ (k,n) $-Absorbing (primary) Hyperideals of a Krasner $ (m,n) $-Hyperring”. Hacettepe Journal of Mathematics and Statistics 52, no. 5 (October 2023): 1229-38. https://doi.org/10.15672/hujms.1199437.
EndNote	Davvaz B, Ulucak G, Tekir Ü (October 1, 2023) Weakly $ (k,n) $-absorbing (primary) hyperideals of a Krasner $ (m,n) $-hyperring. Hacettepe Journal of Mathematics and Statistics 52 5 1229–1238.
IEEE	B. Davvaz, G. Ulucak, and Ü. Tekir, “Weakly $ (k,n) $-absorbing (primary) hyperideals of a Krasner $ (m,n) $-hyperring”, Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 5, pp. 1229–1238, 2023, doi: 10.15672/hujms.1199437.
ISNAD	Davvaz, Bijan et al. “Weakly $ (k,n) $-Absorbing (primary) Hyperideals of a Krasner $ (m,n) $-Hyperring”. Hacettepe Journal of Mathematics and Statistics 52/5 (October 2023), 1229-1238. https://doi.org/10.15672/hujms.1199437.
JAMA	Davvaz B, Ulucak G, Tekir Ü. Weakly $ (k,n) $-absorbing (primary) hyperideals of a Krasner $ (m,n) $-hyperring. Hacettepe Journal of Mathematics and Statistics. 2023;52:1229–1238.
MLA	Davvaz, Bijan et al. “Weakly $ (k,n) $-Absorbing (primary) Hyperideals of a Krasner $ (m,n) $-Hyperring”. Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 5, 2023, pp. 1229-38, doi:10.15672/hujms.1199437.
Vancouver	Davvaz B, Ulucak G, Tekir Ü. Weakly $ (k,n) $-absorbing (primary) hyperideals of a Krasner $ (m,n) $-hyperring. Hacettepe Journal of Mathematics and Statistics. 2023;52(5):1229-38.