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Izv. Vyssh. Uchebn. Zaved. Mat., 2009, Number 4, Pages 43–49 (Mi ivm1319)  

This article is cited in 1 scientific paper (total in 1 paper)

Free algebras of a unary variety with Mal'tsev's operation that satisfies the Pixley conditions

V. L. Usol'tsev

Volgograd State Pedagogical University

Abstract: In this paper we consider the variety $VP$ of algebras with one unary and one ternary operation $p$ that satisfies the Pixley identities, provided that operations are permutable. We describe the structure of a free algebra of the variety $VP$ and study the structure of unary reducts of free algebras. We prove the solvability of the word problem in free algebras and the uniqueness of a free basis; we also describe groups of automorphisms of free algebras. Similar results are obtained for free algebras of a subvariety of the variety $VP$ defined by the identities $p(p(x,y,z),y,z)=p(x,y,z)$ and $p(x,y,p(x,y,z))=p(x,y,z)$.

Keywords: free algebra, ternary Mal'tsev's operation, unar with Mal'tsev's operation, unary reduct, free basis.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:4, 34–39

Bibliographic databases:

UDC: 512.572
Received: 05.12.2006
Revised: 02.02.2008

Citation: V. L. Usol'tsev, “Free algebras of a unary variety with Mal'tsev's operation that satisfies the Pixley conditions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 4, 43–49; Russian Math. (Iz. VUZ), 53:4 (2009), 34–39

Citation in format AMSBIB
\Bibitem{Uso09}
\by V.~L.~Usol'tsev
\paper Free algebras of a~unary variety with Mal'tsev's operation that satisfies the Pixley conditions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2009
\issue 4
\pages 43--49
\mathnet{http://mi.mathnet.ru/ivm1319}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2581473}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2009
\vol 53
\issue 4
\pages 34--39
\crossref{https://doi.org/10.3103/S1066369X09040069}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. L. Usoltsev, “Svobodnye algebry mnogoobraziya unarov s maltsevskoi operatsiei $p$, zadannogo tozhdestvom $p(x,y,x)=y$”, Chebyshevskii sb., 12:2 (2011), 127–134  mathnet  mathscinet
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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