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Siberian Mathematical Journal

, Volume 54, Issue 3, pp 441–445 | Cite as

Interassociativity on a free commutative semigroup

  • A. B. GorbatkovEmail author
Article

Abstract

We describe all interassociates of a free commutative semigroup. Each interassociate of a free commutative semigroup is proved to be a variant of it or coincides with that semigroup. Conditions are found for the isomorphy of two variants of a free commutative semigroup.

Keywords

variant of a semigroup interassociativity free commutative semigroup 

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References

  1. 1.
    Zupnik D., “On interassociativity and related questions,” Aequationes Math., 6, 141–148 (1971).MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Drouzy M., La structuration des ensembles de semigroupes d’ordre 2, 3 et 4 par la relation d’interassociativite. Manuscript (1986).Google Scholar
  3. 3.
    Gould M., Linton K. A., and Nelson A. W., “Interassociates of monogenic semigroups,” Semigroup Forum, 68, 186–201 (2004).MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Hickey J. B., “Semigroups under a sandwich operation,” Proc. Edinburgh Math. Soc., 26, 371–382 (1983).MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Hickey J. B., “On variants of a semigroup,” Bull. Austral. Math. Soc., 34, 447–459 (1986).MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Khan T. A. and Lawson M. V., “Variants of regular semigroups,” Semigroup Forum, 62, 358–374 (2001).MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Magill K. D., “Semigroup structures for families of functions. I. Some homomorphism theorems,” J. Austral. Math. Soc., 7, 81–94 (1967).MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Givens B. N., Linton K. A., Rosin A., and Dishman L., “Interassociates of the free commutative semigroup on n generators,” Semigroup Forum, 74, No. 3, 370–378 (2007).MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Boyd S. J., Gould M., and Nelson A. W., “Interassociativity of semigroups,” in: Proc. Tennessee Topology Conf., World Sci., Singapore, 1997, pp. 33–51.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Luhansk Taras Shevchenko National UniversityLuhanskUkraine

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