Skip to main content
SpringerLink
Log in

A study on a generalization of the n-ary prime hyperideals in a Krasner (m, n)-hyperring

  • Published:
Afrika Matematika Aims and scope Submit manuscript

Abstract

The aim of this research work is to study a generalization of n-ary prime hyperideals in a Krasner (m, n)-hyperring R called n-ary 2-absorbing hyperideals. We will show some properties of them.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ameri, R., Norouzi, M.: Prime and primary hyperideals in Krasner \((m, n)\)-hyperrings. Eur. J. Comb. 34, 379–390 (2013)

    Article  MathSciNet  Google Scholar 

  2. Anbarloei, M.: n-ary 2-absorbing and 2-absorbing primary hyperideals in Krasner (m, n)-hyperideals. MatematiÄ ki Vesnik, (2019). Accepted

  3. Badawi, A.: On 2-absorbing ideals of commutative rings. Bull. Austral. Math. Soc. 75, 417–429 (2007)

    Article  MathSciNet  Google Scholar 

  4. Corsini, S.: Prolegomena of hypergroup theory. Second edition, Aviani editor, Italy (1993)

    MATH  Google Scholar 

  5. Corsini, S., Leoreanu, V.: Applications of hyperstructure theory, Advances in Mathematics, vol. 5. Kluwer Academic Publishers, (2003)

  6. Davvaz, B., Vougiouklis, T.: n-Ary hypergroups. Iran. J. Sci. Technol. Trans. A 30(A2), 165–174 (2006)

    MathSciNet  Google Scholar 

  7. Davvaz, B., Leoreanu-Fotea, V.: Hyperring Theory and Applications. International Academic Press, Palm Harbor (2007)

    MATH  Google Scholar 

  8. Dorente, W.: V. Untersuchungen uber einen verallgemeinerten gruppenbegriff. Math. Z. 29, 1–19 (1928)

    Article  Google Scholar 

  9. Hila, K., Naka, K., Davvaz, B.: On \((k, n)\)-absorbing hyperideals in Krasner \((m, n)\)-hyperrings. Q. J. Math. 69, 1035–1046 (2018)

    Article  MathSciNet  Google Scholar 

  10. Kasner, E.: An extention of the group concept (reported by L. G. Weld). Bull. Am. Math. Soc. 10, 290–291 (1904)

    Google Scholar 

  11. Krasner, M.: A class of hyperrings and hyperfields. Int. J. Math. and Math. Sci. 6, 307–312 (1983)

    Article  MathSciNet  Google Scholar 

  12. Leoreanu, V.: Canonical n-ary hypergroups. Ital. J. Pure Appl. Math., (2008)

  13. Marty, F.: Sur une generalization de la notion de groupe, \(8^{th}\) Congress Math, pp. 45–49. Scandenaves, Stockholm (1934)

    Google Scholar 

  14. Mittas, J.: Hyperstructures canoniques. Mathematica Balkanica 2, 165–179 (1972)

    MathSciNet  MATH  Google Scholar 

  15. Mittas, J.: Hyperstructures et certaines de leurs proprietes, C. R. Acad. Sci. Paris Ser. A-B 269, A623–A626 (1969)

    MathSciNet  Google Scholar 

  16. Mirvakili, S., Davvaz, B.: Applications of the \(\alpha ^\star \)-relation to Krasner hyperrings. J. Algebra 362, 145–156 (2012)

    Article  MathSciNet  Google Scholar 

  17. Mirvakili, S., Davvaz, B.: Constructions of \((m, n)\)-hyperrings. Matematicki Vesnik 67(1), 1–16 (2015)

    MathSciNet  MATH  Google Scholar 

  18. Mirvakili, S., Davvaz, B.: Relations on Krasner \((m, n)\)-hyperring. Eur. J. Comb. 31, 790–802 (2010)

    Article  MathSciNet  Google Scholar 

  19. Omidi, S., Davvaz, B. Contribution to study special kinds of hyperideals in ordered semihyperrings, J. Taibah Univ. Sci., (2016), http://dx.doi.org/10.1016/j.jtusci.2016.09.001

  20. Omid, S., Davvaz, B.: On ordered Krasner hyperrings. Iran. J. Math. Sci. Inform. 12(2), 35–49 (2017)

    MathSciNet  MATH  Google Scholar 

  21. Ostadhadi- Dehkordi, S., Davvaz, B.: A note on isomorphism theorems of Krasner \((m, n)\)- hyperrings. Arab. J. Math. 5, 103–115 (2016)

    Article  MathSciNet  Google Scholar 

  22. Rota, R.: Sugli iperanelli moltiplicativi. Rend. Di Math., Series VII 4, 711–724 (1982)

    MathSciNet  MATH  Google Scholar 

  23. Vougiouklis, T.: Hyperstructures and their representations. Hadronic Press Inc., Florida (1994)

Download references

Author information

Authors and Affiliations

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

    M. Anbarloei

Authors
  1. M. Anbarloei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Anbarloei.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Anbarloei, M. A study on a generalization of the n-ary prime hyperideals in a Krasner (m, n)-hyperring. Afr. Mat. 32, 1021–1032 (2021). https://doi.org/10.1007/s13370-021-00878-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13370-021-00878-6

Keywords

Mathematics Subject Classification

Search

Navigation