Abstract
We construct an additive basis for the relatively free associative algebra F(5)(K) with the Lie nilpotency identity of degree 5 over an infinite domain K containing \({1 \over 6}\). We prove that approximately half of the elements in F(5)(K) are central. We also prove that the additive group of F(5)(ℤ) lacks the elements of simple degree ≥ 5. We find an asymptotic estimation of the codimension of T-ideal, which is generated by the commutator [x1,x2,…,x5] of degree 5.
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Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 1, pp. 175–193.
The author was supported by the Russian Science Foundation (Grant 14-21-00065).
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Pchelintsev, S.V. Construction and Applications of an Additive Basis for the Relatively Free Associative Algebra with the Lie Nilpotency Identity of Degree 5. Sib Math J 61, 139–153 (2020). https://doi.org/10.1134/S0037446620010127
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DOI: https://doi.org/10.1134/S0037446620010127