Semiprime Novikov Algebras

TL;DR

This paper investigates the structure of prime and semiprime Novikov algebras, establishing properties of their nuclei, centers, and ideals, and extending known algebraic results to this class.

Contribution

It proves that prime Novikov algebras have zero nucleus and center, and that ideals of (semi)prime Novikov algebras are (semi)prime, extending classical algebraic properties.

Findings

Prime Novikov algebras have zero nucleus and center.

Ideals of (semi)prime Novikov algebras are (semi)prime.

A minimal ideal is either trivial or simple.

Abstract

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.