On characterizations of a center Galois extension
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200003562 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |