Abstract
1. In the work of A.I. Malcev [2], results of a general nature are applied in particular to the classification of identical relations of degree 3 for associative algebras. It is shown there that, under natural assumptions on the characteristic, any such identical relation is a linear combination of the following relations:
where the summations in relations (1) and (2) are performed over all substitutions, and σ i is the number of inversions in the permutation (i 1, i 2, i 3) of 1, 2, 3.
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References
G. Higman, On a conjecture of Nagata, Proc. Cambridge Philos. Soc. 52, 1 (1956) 1–4.
A.I. Malcev, On algebras with identical defining relations, Mat. Sbornik 26, (1950), no. 1, 19–33.
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Shirshov, A.I. (2009). On Some Identical Relations for Algebras. In: Bokut, L., Shestakov, I., Latyshev, V., Zelmanov, E. (eds) Selected Works of A.I. Shirshov. Contemporary Mathematicians. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8858-4_16
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