If a is an automorphism and delta is a q-skew sigma-derivation of a ring R,
then the subring of invariants is the set R-(delta) = {r is an element of
R / delta(r) = 0}. The main result of this paper is
THEOREM. Let R be a prime algebra with a q-skew sigma-derivation delta, whe
re delta and sigma are algebraic. If R-(delta) satisfies a P.I., then R sat
isfies a P.I.
If delta is separable, then we also obtain the following result:
THEOREM. Let delta be a separable q-skeut sigma-deviation of an algebra R,
where delta and sigma are algebraic.
(i) If R-(delta) satisfies a P.I., then R satisfies a P.I.
(ii) If R-(sigma) boolean AND R-(delta) satisfies a P.I, and a is separable
, then R satisfies a P.I.
When R is a domain, it is necessary to assume neither that a is algebraic n
or that delta is q-skew as we prove
THEOREM. If R is a domain with an algebraic sigma-derivation delta such tha
t R-(delta) satisfies a P.I., then R also satisfies a P.I. (C) 2000 Academi
c Press.