JP Journal of Algebra, Number Theory and Applications
Volume 2, Issue 3, Pages 269 - 283
(December 2002)
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ON COMMUTATOR GALOIS EXTENSIONS
George Szeto (U. S. A.) and Lianyong Xue (U. S. A.)
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Abstract: Let B be a ring with
1, G be a finite automorphism group of
be the
subring of elements in B fixed under
each element in G, and
be the commutator subring of
in B. A structure theorem of
B is given when
is a Galois extension with Galois group
which generalizes a structure of a Galois
algebra, and the study of the commutator
Galois extension B is reduced to the
study of the Galois extension B with
one orbit under the action of G on the
isomorphic summands of B. |
Keywords and phrases: Galois extensions, commutator Galois
extensions, Galois algebras, central Galois algebras,
center Galois extensions. |
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