The nilpotency of the radical in a finitely generated P.I. ring (Q793129)

The Noncommutative Nullstellensatz is well known (Amitsur-Procesi): if R is a finitely generated PI-extension of a commutative Jacobson ring then the radical J(R) is locally nilpotent. In the particular case, when R/J(R) is a commutative ring it was proved by V. N. Latyshev (1977) that J(R) is nilpotent. In this paper the author proves the following outstanding result: Let \(R=\Lambda<a_ 1,...,a_ n>\) be a finitely generated PI-algebra over a central noetherian subring \(\Lambda\). Then the Jacobson radical J(R) is nilpotent. If \(\Lambda\) is a field of characteristic zero then this result is known as theorem of Razmyslov- Kemer, because Yu. P. Razmyslov (1974) proved that the nilpotence of J(R) is equivalent to the existence of a Capelli identity in R and A. R. Kemer proved that R satisfies a Capelli polynomial (1980).