Geodesic
Free algebras of a~unary variety with Mal'tsev's operation that satisfies the Pixley conditions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2009), pp. 43-49

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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. 
@article{IVM_2009_4_a5,
     author = {V. L. Usol'tsev},
     title = {Free algebras of a~unary variety with {Mal'tsev's} operation that satisfies the {Pixley} conditions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {43--49},
     publisher = {mathdoc},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_4_a5/}
}
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V. L. Usol'tsev. Free algebras of a~unary variety with Mal'tsev's operation that satisfies the Pixley conditions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2009), pp. 43-49. http://geodesic.mathdoc.fr/item/IVM_2009_4_a5/