CONSTANTS OF PARTIAL DERIVATIONS AND PRIMITIVE OPERATIONS

Autor(es)

Pchelintsev, S. V. ^{[1, 2]} ; Shestakov, I. P. ^{[3, 1, 4]}

Afiliação do(s) autor(es)

^[1] Sobolev Inst Math, Pr Akad Koptyuga 4, Novosibirsk 630090 - Russia

^[2] Govt Russian Federat, Finance Acad, Leningradskii Pr 49, Moscow 125993 - Russia

^[3] Univ Sao Paulo, BR-05315970 Sao Paulo - Brazil

^[4] Novosibirsk State Univ, Ul Pirogova 1, Novosibirsk 630090 - Russia

• Tipo de documento: Artigo Científico
• Fonte: Algebra and Logic; v. 56, n. 3, p. 210-231, JUL 2017.
• Citações Web of Science: 1

Resumo

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. (AU)

• Processo FAPESP: 14/09310-5 - Estruturas algébricas e suas representações
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Temático