The Galois algebras and the Azumay Galois extensions
Let B be a Galois algebra over a commutative ring R with Galois group G, C the center of B, K={g∈G|g(c)=c for all c∈C}, Jg{b∈B|bx=g(x)b for all x∈B} for each g∈K, and BK=(⊕∑g∈K Jg). Then BK is a central weakly Galois algebra with Galois group induced by K. Moreover, an Azumaya Galois extension B wi...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202110386 |
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| _version_ | 1832564129903149056 |
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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 Galois algebra over a commutative ring R with Galois group G, C the center of B, K={g∈G|g(c)=c for all c∈C}, Jg{b∈B|bx=g(x)b for all x∈B} for each g∈K, and BK=(⊕∑g∈K Jg). Then BK is a central weakly Galois algebra with Galois group induced by K. Moreover, an Azumaya Galois extension B with Galois group K is characterized by using BK. |
| format | Article |
| id | doaj-art-8019cd7a44604057857f3d20cf447200 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8019cd7a44604057857f3d20cf4472002025-02-03T01:11:46ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01311374210.1155/S0161171202110386The Galois algebras and the Azumay Galois extensionsGeorge Szeto0Lianyong Xue1Department of Mathematics, Bradley University, Peoria IL 61625, USADepartment of Mathematics, Bradley University, Peoria IL 61625, USALet B be a Galois algebra over a commutative ring R with Galois group G, C the center of B, K={g∈G|g(c)=c for all c∈C}, Jg{b∈B|bx=g(x)b for all x∈B} for each g∈K, and BK=(⊕∑g∈K Jg). Then BK is a central weakly Galois algebra with Galois group induced by K. Moreover, an Azumaya Galois extension B with Galois group K is characterized by using BK.http://dx.doi.org/10.1155/S0161171202110386 |
| spellingShingle | George Szeto Lianyong Xue The Galois algebras and the Azumay Galois extensions International Journal of Mathematics and Mathematical Sciences |
| title | The Galois algebras and the Azumay Galois extensions |
| title_full | The Galois algebras and the Azumay Galois extensions |
| title_fullStr | The Galois algebras and the Azumay Galois extensions |
| title_full_unstemmed | The Galois algebras and the Azumay Galois extensions |
| title_short | The Galois algebras and the Azumay Galois extensions |
| title_sort | galois algebras and the azumay galois extensions |
| url | http://dx.doi.org/10.1155/S0161171202110386 |
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