ABSTRACT
For a finite-dimensional Hopf algebra H over a field k and an H-comodule algebra A, we study properties of A which are preserved when A is twisted by a Hopf 2-cocycle σ on H. We prove that if there exists σ such that Aσ is super-commutative, then A being affine impies that A is Noetherian. If also Hσ is commutative, then A is integral over a central subring of AcoH . We also consider when A satisfies a polynomial identity.
