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