Skip to main content
SpringerLink
Log in

On filters in eBE-algebras

  • Published:
Afrika Matematika Aims and scope Submit manuscript

Abstract

In this paper, we introduce commutative, medial, normal, irreducible and prime filters in eBE-algebras, and investigate some of them properties. We define and study the concept of commutative eBE-algebra. In particular, we show that every commutative eBE-algebra is a commutative BE-algebra and prove that each filter of such algebra is commutative. Moreover, we give a construction of quotient eBE-algebras via normal filters.

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

Fig. 1

Similar content being viewed by others

Data Availability

No data were used to support this study.

References

  1. Ahn, S.S., So, K.S.: On ideals and upper sets in BE-algebras. Sci. Math. Jpn. 68, 279–287 (2008)

    MathSciNet  MATH  Google Scholar 

  2. Borumand Saeid, A., Rezaei, A., Borzooei, R.A.: Some types of filters in BE-algebras. Math. Comput. Sci. 7, 341–352 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Hu, Q.P., Li, X.: On BCH-algebras. Math. Seminar Notes 11, 313–320 (1983)

    MathSciNet  MATH  Google Scholar 

  4. Imai, Y., Iséki, K.: On axiom systems of propositional calculi XIV. Proc. Japan Acad. 42, 19–22 (1966)

    MathSciNet  MATH  Google Scholar 

  5. Iséki, K.: An algebra related with a propositional calculus. Proc. Japan Acad. 42, 26–29 (1966)

    MathSciNet  MATH  Google Scholar 

  6. Jun, Y.B., Roh, E.H., Kim, H.S.: On BH-algebras. Sci. Math. Jpn. 1, 347–354 (1998)

    MathSciNet  MATH  Google Scholar 

  7. Kim, H.S., Kim, Y.H.: On BE-algebras. Sci. Math. Jpn. 66, 113–116 (2007)

    MathSciNet  MATH  Google Scholar 

  8. Komori, Y.: The class of BCC-algebras is not a variety. Math. Jpn. 29, 391–394 (1984)

    MathSciNet  MATH  Google Scholar 

  9. McKenzie, R.N., McNulty, G.F., Taylor, W.F.: Algebras, Lattices, Varieties. Wadsworth & Brooks/Cole, Monterey (1987)

    MATH  Google Scholar 

  10. Meng, B.L.: CI-algebras. Sci. Math. Jpn. 71, 11–17 (2010)

    MathSciNet  MATH  Google Scholar 

  11. Meng, B.L.: On filters in BE-algebras. Sci. Math. Jpn. 71, 1201–1207 (2010)

    MathSciNet  Google Scholar 

  12. Rezaei, A., Borumand Saeid, A., Radfar, A.: On eBE-algebras. TWMS J. Pure Appl. Math. 7, 200–210 (2016)

    MathSciNet  MATH  Google Scholar 

  13. Rezaei, A., Borumand Saeid, A.: Commutative ideals in BE-algebras. Kyungpook Math. J. 52, 483–494 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. Rezaei, A., Borumand Saeid, A., Borzooei, R.A.: Relation between Hilbert algebras and BE-algebras. Appli. Appli. Math. 8, 573–584 (2013)

    MathSciNet  MATH  Google Scholar 

  15. Rezaei, A., Radfar, A., Pourabdollah, A.: Medial filters in BE-algebras. Alg. Struc. Appl. 7, 127–141 (2020)

    MATH  Google Scholar 

  16. Walendziak, A.: On commutative BE-algebras. Sci. Math. Jpn. 69, 585–588 (2008)

    MathSciNet  MATH  Google Scholar 

  17. Walendziak, A.: On normal filters and congruence relations in BE-algebras. Comment. Math. 52, 199–205 (2012)

    MathSciNet  MATH  Google Scholar 

  18. Ye, R.: On BZ-algebras. In: Selected papers on BCI/BCK-algebras and Computer Logic, Shanghai Jiaotong Univ., pp. 21–24 (1991)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Payame Noor University, P.o.box. 19395-4697, Tehran, Iran

    Akbar Rezaei

  2. Institute of Mathematics, Faculty of Exact and Natural Sciences, Siedlce University of Natural Sciences and Humanities, 3 Maja 54, 08110, Siedlce, Poland

    Andrzej Walendziak

  3. Department of Basic Courses, Xian University of Science and Technology, Xian, 710054, People’s Republic of China

    Biao Long Meng

Authors
  1. Akbar Rezaei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrzej Walendziak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Biao Long Meng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Akbar Rezaei.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rezaei, A., Walendziak, A. & Meng, B.L. On filters in eBE-algebras. Afr. Mat. 34, 56 (2023). https://doi.org/10.1007/s13370-023-01099-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13370-023-01099-9

Keywords

Mathematics Subject Classification

Search

Navigation