Geodesic
Speciality of Metabelian Mal''tsev Algebras
Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 257-266

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It is proved that, for any metabelian Mal'tsev algebra $M$ over a field of characteristic $\ne2,3$, 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 $[x,y][z,t] = 0$. 
@article{MZM_2003_74_2_a7,
     author = {S. V. Pchelintsev},
     title = {Speciality of {Metabelian} {Mal''tsev} {Algebras}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {257--266},
     publisher = {mathdoc},
     volume = {74},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a7/}
}
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S. V. Pchelintsev. Speciality of Metabelian Mal''tsev Algebras. Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 257-266. http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a7/