Minimal identities of octonion algebras
Let \(K\) be a field of a characteristic not \(2, 3\) or \(5\). The main theorem in the paper is an analog of the Amitsur-Levitzki theorem namely: There are no identities of degrees less than 5 for the octonion algebras over \(K\). The author has proved that all identities of degree \(5\) for the octonion algebras follow from the identities \([[x,y]^ 2, z]=0\) and \(x^ 2 S^ +_ 3(y,z,w)-x S^ +_ 3(y,z,w)\circ x=0\) where \(S^ +_ n(x_ 1,...,x_ n)\) is the Jordan standard identity.
scientific article; zbMATH DE number 4061462