On when a graded ring is graded equivalent to a crossed product

Haefner, Jeremy

doi:10.1090/S0002-9939-96-03138-3

On when a graded ring is graded equivalent to a crossed product
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Proc. Amer. Math. Soc. 124 (1996), 1013-1021 Request permission

Abstract:

Let $R$ be a ring graded by a group $G$. We are concerned with describing those $G$-graded rings that are graded equivalent to $G$-crossed products. We give necessary and sufficient conditions for when a strongly graded ring is graded equivalent to a crossed product, provided that the 1-component is either Azumaya or semiperfect. Our result uses the torsion product theorem of Bass and Guralnick. We also construct various examples of such rings.

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