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Constants of derivations on free associative algebras

Published online by Cambridge University Press:  18 July 2002

Vitor de Oliveira Ferreira
Vitor de Oliveira Ferreira
Affiliation:
Departamento de Matemática, Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, São Paulo - SP, 05315-970, Brazil e-mail: vofer@ime.usp.br
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It is proved that the subalgebra of constants of a derivation on a free associative algebra in prime characteristic is free provided that some constraining conditions are satisfied. As a particular case, it follows that the constants of the partial derivatives on a free algebra form a free subalgebra. The main result is also applied in order to provide a simplified proof of a previous result by the author on extensions of tensor rings.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 44 , Issue 1 , January 2002 , pp. 177 - 183
Copyright
2002 Glasgow Mathematical Journal Trust