On characterizations of a center Galois extension

George Szeto and Lianyong Xue

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 23, 1-6

Abstract:

Let B be a ring with 1 , C the center of B , G a finite automorphism group of B , and B G the set of elements in B fixed under each element in G . Then, it is shown that B is a center Galois extension of B G (that is, C is a Galois algebra over C G with Galois group G | C ≅ G ) if and only if the ideal of B generated by { c − g ( c ) | c ∈ C } is B for each g ≠ 1 in G . This generalizes the well known characterization of a commutative Galois extension C that C is a Galois extension of C G with Galois group G if and only if the ideal generated by { c − g ( c ) | c ∈ C } is C for each g ≠ 1 in G . Some more characterizations of a center Galois extension B are also given.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:978696

DOI: 10.1155/S0161171200003562

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