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 -