JP Journal of Algebra, Number Theory and Applications
Volume 6, Issue 3, Pages 597 - 607
(December 2006)
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ON CHARACTERIZATIONS OF A COMMUTATOR GALOIS EXTENSION
Lianyong Xue (U. S. A.)
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Abstract: Let B be a ring with 1, C be the center of B, G be a finite automorphism group of B, be the set of elements in B fixed under each element in G, and be the commutator subring of in B. Then B is called a commutator Galois extension with Galois group G if is a Galois extension with Galois group It is shown that B is a commutator Galois extension with Galois group G if and only if B is a Galois extension with Galois group G such that This generalizes a result for center Galois extensions. |
Keywords and phrases: Galois extensions, center Galois extensions, Azumaya Galois extensions, commutator Galois extensions, Azumaya algebras, Hirata separable extensions. |
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