Hereditary crossed products

Haefner, Jeremy; Janusz, Gerald

doi:10.1090/S0002-9947-00-02476-4

Hereditary crossed products
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by Jeremy Haefner and Gerald Janusz

Trans. Amer. Math. Soc. 352 (2000), 3381-3410

DOI: https://doi.org/10.1090/S0002-9947-00-02476-4

Published electronically: March 27, 2000

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Abstract:

We characterize when a crossed product order over a maximal order in a central simple algebra by a finite group is hereditary. We need only concentrate on the cases when the group acts as inner automorphisms and when the group acts as outer automorphisms. When the group acts as inner automorphisms, the classical group algebra result holds for crossed products as well; that is, the crossed product is hereditary if and only if the order of the group is a unit in the ring. When the group is acting as outer automorphisms, every crossed product order is hereditary, regardless of whether the order of the group is a unit in the ring.

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