Free dimonoids

  • A. V. Zhuchok

We characterize the least semilattice congruence of a free dimonoid and prove that a free dimonoid is a semilattice of s-simple subdimonoids each of which is a rectangular band of subdimonoids.


Triple System Bijective Mapping Leibniz Algebra Rectangular Band Free Semigroup 
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.


  1. 1.
    J.-L. Loday, “Une version non commutative des algèbres de Lie: les algèbres de Leibniz,” Enseign. Math., 39, 269–293 (1993).MathSciNetzbMATHGoogle Scholar
  2. 2.
    J.-L. Loday, “Dialgebras,” in: J.-L. Loday, A. Frabetti, F. Chapoton, and F. Goichot (editors), Dialgebras and Related Operads, Springer (2001), pp. 7–66.Google Scholar
  3. 3.
    P. S. Kolesnikov, “Varieties of dialgebras and conformal algebras,” Sib. Mat. Zh., 49, No. 2, 322–339 (2008).MathSciNetCrossRefGoogle Scholar
  4. 4.
    R. Felipe, Generalized Loday Algebras and Digroups, Comunicaciones del CIMAT, No. I-04-01/21-01-2004 (2004).Google Scholar
  5. 5.
    A. P. Pozhidaev, “Dialgebras and related triple systems,” Sib. Mat. Zh., 49, No. 4, 870–885 (2008).MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    J. D. Phillips, “A short basis for the variety of digroups,” Semigroup Forum, 70, 466–470 (2005).MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    A. V. Zhuchok, “Commutative dimonoids,” Algebra Discr. Math., No. 2, 116–127 (2009).Google Scholar
  8. 8.
    A. V. Zhuchok, “Free commutative dimonoids,” Algebra Discr. Math., 9, No. 1, 109–119 (2010).MathSciNetGoogle Scholar
  9. 9.
    A. V. Zhuchok, “Dibands of subdimonoids,” Mat. Stud., 33, 120–124 (2010).zbMATHGoogle Scholar
  10. 10.
    A. V. Zhuchok, “The least semilattice congruence of a dimonoid,” Visn. Kyiv. Univ., Ser. Fiz.-Mat., Issue 3, 22–24 (2009).Google Scholar
  11. 11.
    M. Yamada, “On the greatest semilattice decomposition of a semigroup,” Kodai Math. Sem. Rep., 7, 59–62 (1955).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  • A. V. Zhuchok
    • 1
  1. 1.Shevchenko Kyiv National UniversityKyivUkraine

Personalised recommendations