Lie nilpotent and solvable associative algebras

Abstract

First we consider nine properties of an associative algebra analogous to properties of nilpotent Lie algebras and connected nilpotent algebraic groups. We demonstrate the order of implication of these properties and that all nine properties are equivalent when the ground field is algebraically closed.Next we consider eight properties of an associative algebra analogous to properties of solvable Lie algebras of characteristic zero and connected solvable algebraic groups of any characteristic. We demonstrate the order of implication of these properties and that all eight properties are equivalent when the ground field is algebraically closed and of characteristic different from 2.