The standard identity in characteristic \(p\): A conjecture of I. B. Volichenko
The main result of this interesting paper is to answer in the affirmative the conjecture of I. B. Volichenko that any PI-algebra over a field of positive characteristic satisfies the standard identity. This means (in contrast to the case of characteristic 0) that in positive characteristic the standard identity cannot be used for the characterization of the \(T\)- ideals of the identities satisfied by a finitely generated algebra. As a consequence of the proof the author establishes the nice result that any PI-algebra over a field of positive characteristic satisfies the same multilinear polynomial identities as some nil-algebra of bounded index.
scientific article; zbMATH DE number 410022