Abstract
It is proved that, for any metabelian Mal'tsev algebra M over a field of characteristic ≠2,3, there is an alternative algebra A such that the algebra M can be embedded in the commutator algebra A(-). Moreover, the enveloping alternative algebra A can be found in the variety of algebras with the identity [x,y][z,t] = 0. The proof of this result is based on the construction of additive bases of the free metabelian Mal'tsev algebra and the free alternative algebra with the identity [x,y][z,t] = 0.
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Pchelintsev, S.V. Speciality of Metabelian Mal'tsev Algebras. Mathematical Notes 74, 245–254 (2003). https://doi.org/10.1023/A:1025060325794
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DOI: https://doi.org/10.1023/A:1025060325794