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 derivat ion of R. We examine the relationship between R and the algebra of con stants 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 ob tain results about fixed subrings of algebraic automorphisms. For inst ance, 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 fi xed subring R(sigma) is Artinian. (C) 1995 Academic Press, Inc.