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In 1974 Kharchenko proved that if a 0 -component of an n -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 ₂ -graded Novikov algebra N=A+M and prove that if the characteristic of the basic field is not 2 or 3 and its 0-component A is associative or Lie-nilpotent of index 3 then the commutator ideal N, N is solvable.
Panasenko et al. (Fri,) studied this question.