On Solvability of Noncommutative Power-Associative Nilalgebras

AbstractWe show that noncommutative power-associative nilalgebras of finite dimension n and nilindex k are solvable if k=n+1 or k=n. For any given integer n>2, we present an example of a power-associative nilalgebra of dimension n and nilindex n−1 which is not solvable. This implies a power-associative nilalgebra of dimension n and nilindex k need not be solvable if k