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Constants of Partial Derivations and Primitive Operations

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Algebra and Logic Aims and scope

We describe algebras of constants of the set of all partial derivations in free algebras of unitarily closed varieties over a field of characteristic 0. These constants are also called proper polynomials. It is proved that a subalgebra of proper polynomials coincides with the subalgebra generated by values of commutators and Umirbaev–Shestakov primitive elements pm,n on a set of generators for a free algebra. The space of primitive elements is a linear algebraic system over a signature Σ = {[x, y], pm,n | m, n ≥ 1}. We point out bases of operations of the set Σ in the classes of all algebras, all commutative algebras, right alternative and Jordan algebras.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    S. V. Pchelintsev & I. P. Shestakov

  2. Finance Academy under the Government of the Russian Federation, Leningradskii pr. 49, Moscow, 125993, Russia

    S. V. Pchelintsev

  3. Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090, Russia

    I. P. Shestakov

  4. Universidade de São Paulo, São Paulo-SEP, 05315-970, Brazil

    I. P. Shestakov

Authors
  1. S. V. Pchelintsev
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  2. I. P. Shestakov
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Correspondence to S. V. Pchelintsev.

Additional information

Supported by Russian Science Foundation, project No. 14-21-00065.

Supported by FAPESP (project No. 2014/09310-5) and by CNPq (project No. 303916/2014-1).

Translated from Algebra i Logika, Vol. 56, No. 3, pp. 317-347, May-June, 2017.

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Pchelintsev, S.V., Shestakov, I.P. Constants of Partial Derivations and Primitive Operations. Algebra Logic 56, 210–231 (2017). https://doi.org/10.1007/s10469-017-9441-x

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  • DOI: https://doi.org/10.1007/s10469-017-9441-x

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