  We study prime and semiprime Novikov algebras. We prove that prime
nonassociative Novikov algebra has zero nucleus and center. It is well known
that an ideal of an alternative (semi)prime algebra is (semi)prime algebra. We
proved this statement for Novikov algebras. It implies that a Baer radical
exists in a class of Novikov algebras. Also, we proved that a minimal ideal of
Novikov algebra is either trivial, or a simple algebra.
