J-hyperideals and related generalizations ‎in ‎ ‎multiplicative ‎hyperrings

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Sciences, Imam Khomeini International University, Qazvin, Iran

Abstract

‎In this paper‎, ‎we define the concept of $J$-hyperideals which is a generalization of $n$-hyperideals‎. ‎A proper hyperideal $I$ of a multiplicative hyperring $R$ is said to be a $J$-hyperideal if $x,y\in R$ such that $x \circ y \subseteq I$‎, ‎then either $x \in J(R)$ or $y \in I$‎. ‎We study and investigate the behavior of the $J$-hyperideals to introduce several results‎. ‎Moreover‎, ‎we extend the notion of $J$-hyperideals to quasi $J$-hyperideals and 2-absorbing $J$-hyperideals‎.
‎Various characterizations of them are provided‎.

Keywords

Main Subjects

References

[1] Akbiyik, S. Y. (2021). Codes over the multiplicative hyperrings. Turkic World Mathematical Society Journal of Applied and Engineering Mathematics, 11(4), 1260-1267.
[2] Ameri, R., & Norouzi, M. (2014). On commutative hyperrings. Int. Journal of Algebraic Hyperstructures and its Applications, 1(1), 45-58.
[3] Ameri, R., & Kordi, A. (2015). Clean multiplicative hyperrings. Italian Journal of Pure and Applied Mathematics, (35), 625-636.
[4] Ameri, R., & Kordi, A. (2016). On regular multiplicative hyperrings. European Journal of Pure and Applied Mathematics, 9(4), 402-418.
[5] Ameri, R., Kordi, A., & Hoskova-Mayerova, S. (2017). Multiplicative hyperring of fractions and coprime hyperideals. An. St. Univ. Ovidius Constanta, 25(1), 5-23.
[6] Anbarloei, M. (2017). On 2-absorbing and 2-absorbing primary hyperideals of a multiplicative hyperring. Research in Mathematics, (4), 1-8.
[7] Anbarloei, M. (2018). On 2-absorbing quasi primary hyperideals of a multiplicative hyperring. JP Journal of Algebra, Number Theory and Applications, 40(4), 575-586.
[8] Anbarloei, M. (2021). A note on two classes of hyperideals. Jordan Journal of Mathematics and Statistics, 14(4), 755-775.
[9] Dasgupta, U. (2007). On prime and primary hyperideals of a multiplicative hyperrings. Bull. Austral. Math. Soc., 75, 417-429.
[10] Dasgupta, U. (2012). On certain classes of hypersemirings, [PhD thesis]. University of Calcutta, Kolkata, India.
[11] Davvaz, B., & Leoreanu-Fotea, V. (2007). Hyperring Theory and Applications. International Academic Press. Palm Harbor, USA.
[12] Ghiasvand, P. (2014). On 2-absorbing hyperideals of multiplicative hyperrings. Second Seminar on Algebra and its Applications, 58-59.
[13] Ghiasvand, P., & Farzalipour, F. (2021). On S-prime hyperideals in multiplicative hyperrings. Journal of Algebraic Hyperstructures and Logical Algebras, 2(2), 25-34.
[14] Kamali Ardakani, L., & Davvaz, B. (2014). Di erential multiplicative hyperring. J. Algebraic Systems, 2(1), 21-35.
[15] Khashan, H. A., & Bani-Ata, A. B. (2021). J-ideals of commutative rings. International Electronic Journal of Algebra, 29, 148-164.
[16] Marty, F. (1934). Sur une generalization de la notion de groupe. 8th Congress Math. Scandenaves, Stockholm, 45-49.
[17] Procesi, R., & Rota, R. (2013). Polynomials over multiplicative hyperring. Discrete Mathematical Sciences and Cryptography, 6, 217-225.
[18] Procesi, R., & Rota, R. (1999). On some classes of hyperstructures. Discrete Mathematics, 208-209(28), 485-497.
[19] Rota, R. (1990). Strongly distributive multiplicative hyperrings. J. of Geom., 39, 130-138.
[20] Rota, R. (1982). Sugli iperanelli moltiplicativi. Rend. Di Math., Series VII, 4, 711-724.
[21] Soltani, Z., Ameri, R., & Talebi Rostami, Y. (2018). An introduction to zero-divisor graphs of a commutative multiplicative hyperring. Sigma J Eng and Nat Sci, 9(1), 101-106.
[22] Tekir, U., Koc, S., & Oral, K. H. (2017). n-ideals of commutative rings. Filomat, 31(10), 2933-2941.
[23] Ulucak, G. (2019). On expansions of prime and 2-absorbing hyperideals in multiplicative hyperrings. Turkish Journal of Mathematics, 43, 1504-1517.

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History

  • Receive Date: 16 December 2023
  • Revise Date: 19 March 2024
  • Accept Date: 17 May 2024

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