Properties of algebras of primary order with one ternary Mal'tsev operation (Q1908453)
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scientific article; zbMATH DE number 848947
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Properties of algebras of primary order with one ternary Mal'tsev operation |
scientific article; zbMATH DE number 848947 |
Statements
Properties of algebras of primary order with one ternary Mal'tsev operation (English)
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27 March 1996
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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.
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Mal'tsev operations
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primary \(p\)-algebras
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solvable \(p\)-algebra
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ternary operation
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subdirect product
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