INVARIANTS OF U-Q(SL(2)) AND Q-SKEW DERIVATIONS

If delta is a q-skew derivation of a ring R, then the subring of invar iants is R-(delta) = {r is an element of R \ delta(r) = 0}. We prove T heorem. Let delta be a q-skew derivation which is algebraic in its act ion on the K-algebra R. If R is (sigma,delta)-semiprime and I not equa l 0 is a (sigma,delta)-stable ideal of R, then I-(delta) is a nonnilpo tent ideal of R-(delta). This result is used to examine the actions of the Hopf algebra H = U-q(sl(2)). We show, under certain natural hypot heses, that for any H-stable ideal I not equal 0 of a semiprime ring, the invariants of I under the action of U-q(sl(2)) are nonnilpotent. ( C) 1998 Elsevier Science B.V. All rights reserved.