Invariant Wedderburn factors
Earl Jay Taft · Illinois Journal of Mathematics · 1957
The Wedderburn principal theorem for a class of algebras states that if an algebra modulo its radical is separable, then it contains a subalgebra with the same structure as the difference algebra.We wish to investigate the problem of when such a subalgebra is invariant under a group of operators on the algebra.The natural setting for this question is that of the extensions of an algebra.In section 2, conditions are given on the groups and algebras considered, which guarantee the existence of such subalgebras.In section 3, a special case of the main theorem for alternative algebras is used to give a proof of the Wedderburn principal theorem for Jordan algebras of charac- teristic not two.In section 4, a uniqueness theorem is given for a special case" self-adjoint Wedderburn factors of an associative algebra over a field of characteristic zero.The author would like to express his appreciation to Professor Nathan Jacobson who suggested these problems and acted as thesis advisor during the preparation of this material.