On Azumaya algebras with a finite automorphism group

George Szeto and Lianyong Xue

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 26, 1-6

Abstract:

Let B be a ring with 1, C the center of B , and G a finite automorphism group of B . It is shown that if B is an Azumaya algebra such that B = ⊕ ∑ g ∈ G J g where J g = { b ∈ B | b x = g ( x ) b for all x ∈ B } , then there exist orthogonal central idempotents { f i ∈ C | i = 1 , 2 , … , m for some integer m } and subgroups H i of G such that B = ( ⊕ ∑ i = 1 m B f i ) ⊕ D where B f i is a central Galois algebra with Galois group H i | B f i ≅ H i for each i = 1 , 2 , … , m and D is contained in C .

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:470967

DOI: 10.1155/S0161171201006068

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