On central commutator Galois extensions of rings
Let B be a ring with 1, G a finite automorphism group of B of order n for some integer n, BG the set of elements in B fixed under each element in G, and Δ=VB(BG) the commutator subring of BG in B. Then the type of central commutator Galois extensions is studied. This type includes the types of Az...
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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/S0161171200004099 |
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| Summary: | Let B be a ring with 1, G a finite automorphism group of B of order n for some integer n,
BG the set of elements in B fixed under each element in G, and
Δ=VB(BG) the
commutator subring of BG in B. Then the type of central
commutator Galois extensions is studied. This type includes the
types of Azumaya Galois extensions and Galois H-separable
extensions. Several characterizations of a central commutator
Galois extension are given. Moreover, it is shown that when G is
inner, B is a central commutator Galois extension of BG if and
only if B is an H-separable projective group ring BGGf.
This generalizes the structure theorem for central Galois algebras
with an inner Galois group proved by DeMeyer. |
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| ISSN: | 0161-1712 1687-0425 |