Exponential growth for codimensions of some p.i. algebras

By the Giambruno-Zaicev theorem for associative p.i. algebras, the exponent ial rate of growth of the codimensions of such a p.i. algebra is always a p ositive integer. Here we calculate that integer for various generic p.i. al gebras which are given by a single identity. These include Capelli-type ide ntities and the various powers of the standard polynomials. (C) 2001 Academ ic Press.