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The endomorphism monoid of a free trioid of rank 1

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Abstract

We describe all endomorphisms of a free trioid of rank 1 and construct a semigroup which is isomorphic to the endomorphism monoid of such free trioid. Also, we give an abstract characteristic for the endomorphism monoid of a free trioid of rank 1 and prove that free trioids are determined by their endomorphism monoids.

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References

  1. Casas J.M.: Trialgebras and Leibniz 3-algebras. Boletin de la Sociedad Matematica Mexicana 12, 165–178 (2006)

    MathSciNet  MATH  Google Scholar 

  2. Formanek E.: A question of B. Plotkin about the semigroup of endomorphisms of a free group. Proceedings of the AMS 130, 935–937 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. Gluskin, L.M.: Ideals of semigroups. Math. Sbornik 55(97), no. 4, 421–448 (1961) (Russian)

  4. Loday J.-L.: Dialgebras, In: Dialgebras and related operads. Lecture Notes in Math. 1763, 7–66 (2001)

    Article  MATH  Google Scholar 

  5. Loday J.-L., Ronco M.O.: Trialgebras and families of polytopes. Contemp. Math. 346, 369–398 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Mashevitzky G., Schein B.M.: Automorphisms of the endomorphism semigroup of a free monoid or a free semigroup. Proc. Amer. Math. Soc. 131, 1655–1660 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. Novelli J.-C., Thibon J.-C.: Construction de trigbres dendriformes. C. R. Math. Acad. Sci. Paris 342, 365–369 (2006)

    Article  MathSciNet  Google Scholar 

  8. Novikov B.V.: Semigroups of cohomological dimension one. J. Algebra 204, 386–393 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  9. Pozhidaev A.P.: Dialgebras and related triple systems. Sib. Math. J. 49, 696–708 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Shevrin, L.N.: Densely embedded ideals. Math. Sbornik 79(121), no. 3(7), 425–432 (1969) (Russian)

  11. Usenko, V.M.: Semigroups of endomorphisms of free groups. Problems in Algebra, Gomel: Izv. Gomelskogo universiteta 3, no. 16, 182–185 (2000) (Russian)

  12. Zhuchok, A.V.: Free trioids. Bulletin of University of Kyiv, Ser. Physics and Mathematics 4, 23–26 (2010) (Ukrainian)

  13. Zhuchok A.V.: Some congruences on trioids. J. Math. Sci. (N.Y.) 187, 138–145 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhuchok, Yu.V.: Representations of ordered dimonoids by binary relations. Asian-Eur. J. Math. 7, no.1, 1450006 (13 pp.) (2014)

  15. Zhuchok, Yu.V.: On definability of free trioids by endomorphism semigroups. Dopovidi NANU 4, 7–11 (2015) (Russian)

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska 60, Kyiv, 01601, Ukraine

    Yurii V. Zhuchok

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  1. Yurii V. Zhuchok
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Correspondence to Yurii V. Zhuchok.

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Presented by M. Jackson.

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Zhuchok, Y.V. The endomorphism monoid of a free trioid of rank 1. Algebra Univers. 76, 355–366 (2016). https://doi.org/10.1007/s00012-016-0392-1

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  • DOI: https://doi.org/10.1007/s00012-016-0392-1

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