PI-algebras and their cocharacters

AbstractAll PI-algebras R satisfy identities of the form: f∗[x, y] = Σ ασxσ(1)y1xσ(2)y2 … yn − 1xσ(n) (Theorem A.) The existence of these identities imply also that cocharacters xn(R) lie in a hook-shaped strip of width depending on the degree of the minimal identity of R (Theorem C). This extends a characterization of rings satisfying a Capelli identity (Theorem B)