ON CONSTANTS OF ALGEBRAIC DERIVATIONS AND FIXED-POINTS OF ALGEBRAIC AUTOMORPHISMS

Let R be a semiprime algebra over a field F and d an algebraic derivation of R. We examine the relationship between R and the algebra of constants R(d). We prove that: (1) The prime radical B(R(d)) is nilpotent with the index of nilpotency depending on the minimal polynomial of d; (2) R(d) is Artinian if and only if R is Artinian. Using these we obtain results about fixed subrings of algebraic automorphisms. For instance, we show that if sigma is an automorphism of a prime order p of a semiprime ring R with pR = 0 then R is Artinian if and only if the fixed subring R(sigma) is Artinian. (C) 1995 Academic Press, Inc.