Standard

CONSTANTS OF PARTIAL DERIVATIONS AND PRIMITIVE OPERATIONS. / Pchelintsev, S. V.; Shestakov, I. P.

In: Algebra and Logic, Vol. 56, No. 3, 01.07.2017, p. 210-231.

Research output: Contribution to journal › Article › peer-review

Harvard

Pchelintsev, SV & Shestakov, IP 2017, 'CONSTANTS OF PARTIAL DERIVATIONS AND PRIMITIVE OPERATIONS', Algebra and Logic, vol. 56, no. 3, pp. 210-231. https://doi.org/10.1007/s10469-017-9441-x

APA

Pchelintsev, S. V., & Shestakov, I. P. (2017). CONSTANTS OF PARTIAL DERIVATIONS AND PRIMITIVE OPERATIONS. Algebra and Logic, 56(3), 210-231. https://doi.org/10.1007/s10469-017-9441-x

Vancouver

Pchelintsev SV, Shestakov IP. CONSTANTS OF PARTIAL DERIVATIONS AND PRIMITIVE OPERATIONS. Algebra and Logic. 2017 Jul 1;56(3):210-231. doi: 10.1007/s10469-017-9441-x

Author

Pchelintsev, S. V. ; Shestakov, I. P. / CONSTANTS OF PARTIAL DERIVATIONS AND PRIMITIVE OPERATIONS. In: Algebra and Logic. 2017 ; Vol. 56, No. 3. pp. 210-231.

BibTeX

@article{617ea7b4da374268916572c4a5403273,
title = "CONSTANTS OF PARTIAL DERIVATIONS AND PRIMITIVE OPERATIONS",
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 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 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) vertical bar m, n >= 1}. We point out bases of operations of the set S in the classes of all algebras, all commutative algebras, right alternative and Jordan algebras.",
keywords = "primitive operations, proper polynomials, free algebras, ALGEBRAS, ENVELOPE",
author = "Pchelintsev, {S. V.} and Shestakov, {I. P.}",
year = "2017",
month = jul,
day = "1",
doi = "10.1007/s10469-017-9441-x",
language = "English",
volume = "56",
pages = "210--231",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "3",

}

RIS

TY - JOUR

T1 - CONSTANTS OF PARTIAL DERIVATIONS AND PRIMITIVE OPERATIONS

AU - Pchelintsev, S. V.

AU - Shestakov, I. P.

PY - 2017/7/1

Y1 - 2017/7/1

N2 - 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 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) vertical bar m, n >= 1}. We point out bases of operations of the set S in the classes of all algebras, all commutative algebras, right alternative and Jordan algebras.

AB - 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 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) vertical bar m, n >= 1}. We point out bases of operations of the set S in the classes of all algebras, all commutative algebras, right alternative and Jordan algebras.

KW - primitive operations

KW - proper polynomials

KW - free algebras

KW - ALGEBRAS

KW - ENVELOPE

UR - http://www.scopus.com/inward/record.url?scp=85028521696&partnerID=8YFLogxK

U2 - 10.1007/s10469-017-9441-x

DO - 10.1007/s10469-017-9441-x

M3 - Article

VL - 56

SP - 210

EP - 231

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 3

ER -

ID: 18735056