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Generalized crossed products and Azumaya algebras

โœ Scribed by K.-H Ulbrich

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
812 KB
Volume
136
Category
Article
ISSN
0021-8693

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An algebra \(R\) with anti-isomorphism ( \({ }^{*}\) ) is shown to be Azumaya if (*) is given by an element of \(R \otimes R^{\text {op }}\); in particular, this is the case if the canonical map \(R \otimes_{C} R^{\text {op }} \rightarrow \operatorname{End}_{C}(R)\) is onto. Consequently, the existe

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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 ลฝ call D a crossed product or G G-crossed product if G G is the Galois group of .