on characterizations of a center galois extension
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ID: 149055
2000
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Abstract
Let B be a ring with 1, C the center of B, G a finite
automorphism group of B, and BG the set of elements in B
fixed under each element in G. Then, it is shown that B is a
center Galois extension of BG (that is, C is a Galois algebra
over CG 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 CG 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.
| Reference Key |
szeto2000internationalon
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|---|---|
| Authors | ;George Szeto;Lianyong Xue |
| Journal | structural engineering and mechanics |
| Year | 2000 |
| DOI |
10.1155/S0161171200003562
|
| URL | |
| Keywords |
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