T-Ideais e T-espaços gerados por comutadores.

Abstract

In this work are study the T-ideal T3, generated by the triple commutator, and the T-spaces S2 and S3, generated by the double and triple commutator respectively, of the free unital associative algebra K⟨X⟩, where K is a feld of characteristic zero. In this thesis we show relationships between these spaces and their intersections with the space Pn of the multilinear polynomials of degree n is analyzed. Through the codimensions sequence of the T-space S2 it is also proved that it does not contain any non-zero T-ideal as well as is characterized the T-spaces with this property.