## Abstract

We first deal with classical crossed products S^{f} ^{*} G, where G is a finite group acting on a Dedekind domain S and S^{G} (the G-invariant elements in S) a DVR, admitting a separable residue fields extension. Here f: G × G → S^{*} is a 2-cocycle. We prove that S^{f} * G is hereditary if and only if S/Jac(S)^{f̄} * G is semi-simple. In particular, the heredity property may hold even when S/S^{G} is not tamely ramified (contradicting standard textbook references). For an arbitrary Krull domain S, we use the above to prove that under the same separability assumption, S ^{f} * G is a maximal order if and only if its height one prime ideals are extended from S. We generalize these results by dropping the residual separability assumptions. An application to non-commutative unique factorization rings is also presented.

Original language | English |
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Pages (from-to) | 2733-2742 |

Number of pages | 10 |

Journal | Proceedings of the American Mathematical Society |

Volume | 135 |

Issue number | 9 |

DOIs | |

State | Published - Sep 2007 |

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics