The general Ikehata theorem for H-separable crossed products
Let B be a ring with 1, C the center of B, G an automorphism group of B of order n for some integer n, CG the set of elements in C fixed under G, Δ=Δ(B,G,f) a crossed product over B where f is a factor set from G×G to U(CG). It is shown that Δ is an H-separable extension of B and VΔ(B) is a...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171200003124 |
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| _version_ | 1849691427809787904 |
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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, C the center of B, G an automorphism group of B of order n for some integer n, CG the set of elements in C fixed under G, Δ=Δ(B,G,f) a crossed product over B where f is a factor
set from G×G to U(CG). It is shown that Δ is an
H-separable extension of B and VΔ(B) is a commutative
subring of Δ if and only if C is a Galois algebra over
CG with Galois group G|C≅G. |
| format | Article |
| id | doaj-art-e7c208ae61334bb9b34dcb2545ab8b81 |
| institution | DOAJ |
| 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-e7c208ae61334bb9b34dcb2545ab8b812025-08-20T03:21:02ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-01231065766210.1155/S0161171200003124The general Ikehata theorem for H-separable crossed productsGeorge Szeto0Lianyong Xue1Department of Mathematics, Bradley University, Peoria 61625, Illinois, USADepartment of Mathematics, Bradley University, Peoria 61625, Illinois, USALet B be a ring with 1, C the center of B, G an automorphism group of B of order n for some integer n, CG the set of elements in C fixed under G, Δ=Δ(B,G,f) a crossed product over B where f is a factor set from G×G to U(CG). It is shown that Δ is an H-separable extension of B and VΔ(B) is a commutative subring of Δ if and only if C is a Galois algebra over CG with Galois group G|C≅G.http://dx.doi.org/10.1155/S0161171200003124Crossed productsGalois extensionsH-separable extensions.. |
| spellingShingle | George Szeto Lianyong Xue The general Ikehata theorem for H-separable crossed products International Journal of Mathematics and Mathematical Sciences Crossed products Galois extensions H-separable extensions.. |
| title | The general Ikehata theorem for H-separable crossed products |
| title_full | The general Ikehata theorem for H-separable crossed products |
| title_fullStr | The general Ikehata theorem for H-separable crossed products |
| title_full_unstemmed | The general Ikehata theorem for H-separable crossed products |
| title_short | The general Ikehata theorem for H-separable crossed products |
| title_sort | general ikehata theorem for h separable crossed products |
| topic | Crossed products Galois extensions H-separable extensions.. |
| url | http://dx.doi.org/10.1155/S0161171200003124 |
| work_keys_str_mv | AT georgeszeto thegeneralikehatatheoremforhseparablecrossedproducts AT lianyongxue thegeneralikehatatheoremforhseparablecrossedproducts AT georgeszeto generalikehatatheoremforhseparablecrossedproducts AT lianyongxue generalikehatatheoremforhseparablecrossedproducts |