INVARIANTS OF SKEW DERIVATIONS

If sigma is an automorphism and delta is a sigma-derivation of a ring R, then the subring of invariants is the set R-(delta) = {r is an elem ent of R \ delta(r) = 0}. The main result of this paper is Theorem, Le t delta be a sigma-derivation of an algebra R over a commutative ring K such that delta(n+k)(r) + a(n-1)delta(n+k-1)(r) +...+ a(1) delta(k+1 )(r) + a(0) delta(k)(r) = 0, for all r is an element of R, where a(n-1 ),..., a(1),a(0) is an element of K and a(0)(-1) is an element of K. ( i) If Rn+1 not equal 0, then R(delta) not equal 0. (ii) If L is a delt a-stable left ideal of R such that l.ann(R)(L) = 0, then L(delta) not equal 0. This theorem generalizes results on the invariants of automor phisms and derivations.