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Properties of algebras of primary order with one ternary Mal’tsev operation. (English. Russian original) Zbl 0840.08006

Algebra Logic 34, No. 2, 67-72 (1995); translation from Algebra Logika 34, No. 2, 132-141 (1995).
Algebras with a ternary operation \(p(x,y,z)\) obeying the Mal’tsev identities \(p(x,x,y) = p(y,x,x)\) \(= y\) (\(p\)-algebras) are studied. It is shown that a free solvable \(p\)-algebra is embeddable in a subdirect product of \(p\)-algebras of primary orders. Examples of simple non-Abelian \(p\)-algebras of primary order and of a solvable non-nilpotent \(p\)-algebra of any finite order \(> 5\) are also constructed.
Reviewer: J.Henno (Tallinn)

MSC:

08A40 Operations and polynomials in algebraic structures, primal algebras
08B05 Equational logic, Mal’tsev conditions
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References:

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