### Abstract

In this paper we prove that if G is a finite group of automorphisms of a ring R, where the order of G is a unit in R, then R is fully integral of degree m( G ) over the fixed ring R^{G}. Here m is a function of the order of G. This gives a positive answer to a well-known question of S. Montgomery and extends the result of D. S. Passman for abelian group actions. Our theorem can be viewed as a generalization of the Bergman-Isaacs theorem. In fact that result can be obtained as a corollary, albeit with a poorer index of nilpotence. We then briefly consider duality for Hopf algebra actions and conclude by proving an integrality result for an inner action by a finite-dimensional semisimple Hopf algebra.

Original language | English (US) |
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Pages (from-to) | 206-214 |

Number of pages | 9 |

Journal | Journal of the London Mathematical Society |

Volume | s2-40 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1989 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*Journal of the London Mathematical Society*,

*s2-40*(2), 206-214. https://doi.org/10.1112/jlms/s2-40.2.206