## Abstract

Let if be a Hopf algebra over a field k, and A an H-module algebra over k. Let A^{H} = (a ∈ A|h · a = ε(h)a, all h ∈ H). This paper is mainly concerned with inner actions. We prove the existence of a "symmetric" quotient ring Q of A, which is also an H-module algebra, and consider Q-inner actions, an analogue of X-inner automorphisms. Under certain conditions on A and H we show that Q contains B, a finite-dimensional separable algebra over its center C, a field. Moreover, the centralizer of B in Q is Q^{H}. This is used to prove that if A^{H} is P.I. then so is A, and that A is fully integral over A^{H}C of bounded degree. We also consider connections between the A, A^{H} and A#H module structures.

Original language | English |
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Pages (from-to) | 45-66 |

Number of pages | 22 |

Journal | Pacific Journal of Mathematics |

Volume | 125 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 1986 |

## ASJC Scopus subject areas

- Mathematics (all)