Skip to main content
SpringerLink
Log in

Characterization of binary polynomials of idempotent algebras

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

In this paper, we characterize the set of all binary algebraic (or polynomial) operations of an idempotent algebra that has at least one r-ary algebraic operation, (r ≥ 2), depending on every variable such that there is no an (r+2)-ary algebraic operation depending on at least (r+1) variables. We prove that this set forms a finite Boolean algebra, and then we characterize this Boolean algebra.

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. V. D. Belousov, “Systems of quasigroups with generalized identities,” Usp. Mat. Nauk, 20, No. 1 (121), 75–146 (1965).

    MathSciNet  MATH  Google Scholar 

  2. S. L. Bloom, Z. Ésik, and E. G. Manes, “A Cayley theorem for Boolean algebras,” Am. Math. Mon., 97, No. 9, 831–833 (1990).

    Article  MATH  Google Scholar 

  3. Z. Ésik, “A Cayley theorem for ternary algebras,” Int. J. Algebra Comput., 8, No. 3, 311–316 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  4. Yu. M. Movsisyan, “The multiplicative group of a field and hyperidentities,” Izv. Akad. Nauk SSSR, Ser. Mat., 53, No. 5, 1040–1055 (1989).

    Google Scholar 

  5. Yu. M. Movsisyan, “Superidentities in algebras and varieties,” Usp. Mat. Nauk, 53, No. 1 (319), 61–114 (1998).

    Google Scholar 

  6. Yu. M. Movsisyan, “On the representations of DeMorgan algebras,” in: Trends in Logic III, Studialogica, Warsaw (2005); http://www.ifispan.waw.pl/studialogica/Movsisyan.pdf

  7. Yu. M. Movsisyan, “Binary representations of algebras with at most two binary operations. A Cayley theorem for distributive lattices,” Int. J. Algebra Comput., 19, No. 1, 97–106 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  8. R. Padmanabhan and P. Penner, “Lattice ordered polynomial algebras,” Order, 15, No. 1, 75–86 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  9. J. Pashazadeh, “A characterization of DeMorgan bisemigroup of binary functions,” Int. J. Algebra Comput., 18, No. 5, 951–956 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  10. J. Pashazadeh and Yu. M. Movsisyan, “On the representation of Boolean algebras,” Far East J. Math. Sci., 26, No. 3, 789–794 (2007).

    MathSciNet  MATH  Google Scholar 

  11. S. K. Stein, “On the foundations of quasigroups,” Trans. Am. Math. Soc., 85, 228–256 (1957).

    Article  MATH  Google Scholar 

  12. K. Urbanik, “On algebraic operations in idempotent algebras,” Colloq. Math., 13, 129–157 (1964/1965).

    MathSciNet  Google Scholar 

  13. M. Yoeli and S. Rinon, “Application of ternary algebra to the study of static hazards,” J. ACM, 11 (1), 84–89 (1964).

    Article  MATH  Google Scholar 

  14. K. A. Zaretskii, “Abstract characteristics of bisemigroups of binary operations,” Mat. Zametki, 1, No. 5, 525–530 (1967).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Yerevan State University, Yerevan, Armenia

    Yu. M. Movsisyan

  2. Islamic Azad University, Bonab branch, Bonab, Iran

    J. Pashazadeh

Authors
  1. Yu. M. Movsisyan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Pashazadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu. M. Movsisyan.

Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 74, Proceedings of the International Conference “Modern Algebra and Its Applications” (Batumi, 2010), Part 1, 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Movsisyan, Y.M., Pashazadeh, J. Characterization of binary polynomials of idempotent algebras. J Math Sci 186, 802–804 (2012). https://doi.org/10.1007/s10958-012-1037-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-012-1037-3

Keywords

Search

Navigation