Hereditary crossed products
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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