Advertisement

Journal of Mathematical Sciences

, Volume 193, Issue 3, pp 414–417 | Cite as

Entropic Pairs of Operations and Generalized Endomorphisms

  • A. Ehsani
Article

Abstract

In this paper, we define concepts of entropic pairs of operations and the generalized endomorphism for an algebra and investigate the relationships between them. We characterize entropic pairs of operations of quasigroups and show that in some cases, the presence of a generalized endomorphism is equivalent to the entropic property for an algebra.

Keywords

Abelian Group Binary Operation Unit Element Mediality Identity Entropic Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. Aczél, V. D. Belousov, and M. Hosszú, “Generalized associativity and bisymmetry on quasigroups,” Acta Math. Acad. Sci. Hungar., 11, 127–136 (1960).MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    S. Burris and H. P. Sankappanavar, “A course in universal algebra,” Grad. Texts Math., 78, Springer-Verlag, New York–Berlin (1981).MATHCrossRefGoogle Scholar
  3. 3.
    A. Ehsani, “The generalized entropic property for a pair of operations,” J. Contemp. Math. Anal., 46, No. 1, 56–60 (2011).MathSciNetCrossRefGoogle Scholar
  4. 4.
    J. Jezek and T. Kepka, “Medial groupoids,” Rozpravy Československé Akad. Věd Řada Mat. Přírod. Věd, 93, No. 2 (1983).Google Scholar
  5. 5.
    S. MacLane, Homology, Springer-Verlag (1994).Google Scholar
  6. 6.
    Yu. M. Movsisyan, Introduction to the Theory of Algebras with Hyperidentities [in Russian], Erevan. Univ., Erevan (1986).Google Scholar
  7. 7.
    Yu. M. Movsisyan, Hyperidentities and Hypervarieties in Algebras [in Russian], Erevan. Univ., Erevan (1990).Google Scholar
  8. 8.
    Yu. M. Movsisyan, “Superidentities in algebras and varieties,” Usp. Mat. Nauk, 53, No. 1 (319), 61–114 (1998).MathSciNetCrossRefGoogle Scholar
  9. 9.
    A. Romanowska and J. D. H. Smith, Modes, World Scientific, River Edge, New Jersey (2002).MATHCrossRefGoogle Scholar
  10. 10.
    K. Toyoda, “On axioms of linear functions,” Proc. Imp. Acad. Tokyo, 17, 221–227 (1941).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Islamic Azad UniversityTehranIran

Personalised recommendations