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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| _version_ | 1850161113615826944 |
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| author | George Szeto Lianyong Xue |
| author_facet | George Szeto Lianyong Xue |
| author_sort | George Szeto |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-fb46042c1e034caa8fcdc742fb1cd8ca |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-fb46042c1e034caa8fcdc742fb1cd8ca2025-08-20T02:22:56ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-0124528929410.1155/S0161171200004099On central commutator Galois extensions of ringsGeorge Szeto0Lianyong Xue1Mathematics Department, Bradley University, Peoria, Illinois 61625, USAMathematics Department, Bradley University, Peoria, Illinois 61625, USALet 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.http://dx.doi.org/10.1155/S0161171200004099Azumaya algebrasGalois extensionscentral Galois extensions Azumaya Galois extensionscenter Galois extensionsH-separable extensions. |
| spellingShingle | George Szeto Lianyong Xue On central commutator Galois extensions of rings International Journal of Mathematics and Mathematical Sciences Azumaya algebras Galois extensions central Galois extensions Azumaya Galois extensions center Galois extensions H-separable extensions. |
| title | On central commutator Galois extensions of rings |
| title_full | On central commutator Galois extensions of rings |
| title_fullStr | On central commutator Galois extensions of rings |
| title_full_unstemmed | On central commutator Galois extensions of rings |
| title_short | On central commutator Galois extensions of rings |
| title_sort | on central commutator galois extensions of rings |
| topic | Azumaya algebras Galois extensions central Galois extensions Azumaya Galois extensions center Galois extensions H-separable extensions. |
| url | http://dx.doi.org/10.1155/S0161171200004099 |
| work_keys_str_mv | AT georgeszeto oncentralcommutatorgaloisextensionsofrings AT lianyongxue oncentralcommutatorgaloisextensionsofrings |