Variedades de álgebras associativas de expoente um ou dois.

Abstract

In this work we present a characterization of varieties of associative algebras with exponent less than or equal to two, overelds of characteristic zero. Werst show a result dueto Kemer which states that a variety has expoent lower than or equal to one if, and only if, it does not contain the in finite dimensional Grassmann algebra and the algebra of 2 2 upper triangular matrices overa eld. Finally, we show are sult by Giambruno and Zaicev, which states that a variety has exponent higher than two, if and only if, it contains one of the ve algebras given in a previous list.