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Embedding Division Algebras in Crossed Products

✍ Scribed by Burton Fein; David J. Saltman; Murray Schacher

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
161 KB
Volume
182
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let F be an arbitrary field and let D be a division algebra having center F which is finite dimensional over F. In general, there need not exist a maximal subfield E of D which is Galois over F. If such an E exists, we Ž call D a crossed product or G G-crossed product if G G is the Galois group of . E over F ; if no such E exists, we call D a noncrossed product. There are three primary examples of noncrossed product division algebras in the w x literature; these are the generic division algebras of Amitsur A , the w x w x Jacob᎐Wadsworth examples JW , and the examples of Brussel B1 . Rew x cently, Brussel B2 proved that certain of his noncrossed products cannot be embedded in crossed product division algebras with the same center. ŽWe have also been informed by Adrian Wadsworth that the noncrossed w x . products of JW can be modified to have the same property. This raises

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