We study left ideals of Novikov algebras. It is shown that the center and the associative center of an ideal of a semiprime Novikov algebra are inherited from the whole algebra. We prove that in a prime nonassociative Novikov algebra, every left ideal that does not lie in the right annihilator of the algebra is itself a prime nonassociative Novikov algebra. We also obtain a description of left ideals of a semiprime Novikov algebra. It is shown that a minimal left ideal of a Novikov algebra lies either in the center or in the associator ideal of the algebra.
Kotenkov et al. (2026) studied this question.