Abstract:
Alternative (right) Noetherian algebras are considered. It is proved that, in these algebras, the nil ideals of finite codimension are nilpotent, which generalizes the corresponding Zhevlakov's result. As a corollary, we describe just infinite alternative nonassociative algebras (for the field characteristic distinct from 2).
Keywords:Noetheriaty, nil ideal, alternative algebra, just infinite algebra, exceptional algebra, codimension.