304 research outputs found
On radicals of Novikov algebras
We show that in a prime nonassociative Novikov algebra every nonzero ideal is
non-associative. We prove that Baer (and Andrunakievich) radical and left
quasiregular radical coincide in finite dimensional Novikov algebras over a
field of characteristic 0 or algebraically closed field of odd characteristic.
We show non-existence of right quasiregular radical in finite dimensional
Novikov algebras.Comment: 9 page
Semiprime Novikov Algebras
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.Comment: 11 page
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