Codimensions of generalized polynomial identities

It is proved that for every finite-dimensional associative algebra A over a field of characteristic zero there are numbers C element of Q{sub +} and t element of Z{sub +} such that gc{sub n}(A){approx}Cn{sup t}d{sup n} as n{yields}{infinity}, where d=PI exp(A) element of Z{sub +}. Thus, Amitsur's and Regev's conjectures hold for the codimensions gc{sub n}(A) of the generalized polynomial identities. Bibliography: 6 titles.