HOPF ACTIONS ON FACTOR RINGS AND INDUCED HOPF ACTIONS

Suppose H is a finite dimensional Hopf algebra over a field k and A an H-module algebra. In this paper, we characterize the projectivity of A as an A#K-module and show that if K is a normal subHopfalgebra, t(K) . c = 1 for some c epsilon A and A/A(H) is H-Frobenius, then A(K)/A( H) is (H) over bar -Frobenius. In particular, if A/A(H) is H*-Galois, then A(K)/A(H) is (H) over bar-Glaois, where (H) over bar = H/K+H an d O not equal t(K) epsilon integral(K).