On certain classes of algebras

Abstract

Sugiura [4] and Jόichi [_2~] have studied the classes (A\ (Ak\ &>2 and (AJ) of Lie algebras. In this paper we define these as well as some other classes for general nonassociative algebras and obtain a characterization of alternative algebras over a field of characteristic zero belonging to any one of these classes. Incidentally, we obtain certain results which include striking improvements of earlier ones due to Sugiura (loc. cit.) and Jδichi (loc. cit.).