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.

中文翻译：

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Novikov $ ��_{2} $ 具有关联 0 分量的分级代数

1974 年 Kharchenko 证明，如果\( n \)分级关联代数的\( 0 \)分量是 PI，则该代数就是 PI。在特征为 0 的诺维科夫代数中，多项式恒等式的存在等价于换向器理想的可解性。我们研究一个\( 𝕑_{2} \)分级诺维科夫代数\( N=A+M \)并证明如果基本域的特征不是 2 或 3 及其 0 分量 \( A \)是下标 3 的缔合或李幂零，则理想换向器 \( [N,N] \)是可解的。