The Galois algebras and the Azumay Galois extensions

George Szeto and Lianyong Xue

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 31, 1-6

Abstract:

Let B be a Galois algebra over a commutative ring R with Galois group G , C the center of B , K = { g ∈ G | g ( c ) = c   for all   c ∈ C } , J g { b ∈ B | b x = g ( x ) b   for all   x ∈ B } for each g ∈ K , and B K = ( ⊕ ∑ g ∈ K   J g ) . Then B K is a central weakly Galois algebra with Galois group induced by K . Moreover, an Azumaya Galois extension B with Galois group K is characterized by using B K .

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:106213

DOI: 10.1155/S0161171202110386

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