Novikov -Graded Algebras with an Associative 0-Component.

In 1974 Kharchenko proved that if a -component of an -graded associative algebra is PI then this algebra is PI. In the Novikov algebras of characteristic 0 the existence of a polynomial identity is equivalent to the solvability of the commutator ideal. We study a -graded Novikov algebra and prove that if the characteristic of the basic field is not 2 or 3 and its 0-component is associative or Lie-nilpotent of index 3 then the commutator ideal is solvable. [ABSTRACT FROM AUTHOR]