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Algebra Logika, 2017, Volume 56, Number 3, Pages 317–347 (Mi al794)  

This article is cited in 2 scientific papers (total in 2 papers)

Constants of partial derivations and primitive operations

S. V. Pchelintsevab, I. P. Shestakovacd

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
b Finance Academy under the Government of the Russian Federation, Leningradskii pr. 49, Moscow, 125993 Russia
c Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia
d Universidade de São Paulo, São Paulo-SEP, 05315-970 Basil

Abstract: 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 eigenpolynomials.
It is proved that a subalgebra of eigenpolynomials coincides with the subalgebra generated by values of commutators and Umirbaev–Shestakov primitive elements $p_{m,n}$ on a set of generators for a free algebra.
The space of primitive elements is a linear algebraic system over a signature $\Sigma=\{[x,y],p_{m,n}\mid m,n\ge1\}$. We point out bases of operations of the set $\Sigma$ in the classes of all algebras, all commutative algebras, right alternative and Jordan algebras.

Keywords: primitive operations, eigenpolynomials, free algebras.

Funding Agency Grant Number
Russian Science Foundation 14-21-00065
Fundação de Amparo à Pesquisa do Estado de São Paulo 2014/09310-5
National Council for Scientific and Technological Development (CNPq) 303916/2014-1
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).


DOI: https://doi.org/10.17377/alglog.2017.56.303

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English version:
Algebra and Logic, 2017, 56:3, 210–231

Bibliographic databases:

UDC: 512.554.5
Received: 26.01.2016

Citation: S. V. Pchelintsev, I. P. Shestakov, “Constants of partial derivations and primitive operations”, Algebra Logika, 56:3 (2017), 317–347; Algebra and Logic, 56:3 (2017), 210–231

Citation in format AMSBIB
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\by S.~V.~Pchelintsev, I.~P.~Shestakov
\paper Constants of partial derivations and primitive operations
\jour Algebra Logika
\yr 2017
\vol 56
\issue 3
\pages 317--347
\mathnet{http://mi.mathnet.ru/al794}
\crossref{https://doi.org/10.17377/alglog.2017.56.303}
\transl
\jour Algebra and Logic
\yr 2017
\vol 56
\issue 3
\pages 210--231
\crossref{https://doi.org/10.1007/s10469-017-9441-x}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85028521696}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. V. Pchelintsev, “Identities of metabelian alternative algebras”, Siberian Math. J., 58:4 (2017), 693–710  mathnet  crossref  crossref  isi  elib  elib
    2. S. V. Pchelintsev, “Identities of the model algebra of multiplicity 2”, Siberian Math. J., 59:6 (2018), 1105–1124  mathnet  crossref  crossref  isi  elib
  • Алгебра и логика Algebra and Logic
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