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Division Algebras Not Embeddable in Crossed Products

✍ Scribed by Eric S. Brussel

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 317 KB
Volume: 179
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0029

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✦ Synopsis

We show that division algebras do not always embed in crossed product division algebras, so the latter do not serve as ''Galois closures'' for division algebras. We construct decomposable noncrossed product division algebras of prime-power index over rational function fields and Laurent series fields over number fields. We discover a rigid nonabelian group of order p 4 .

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