The Boolean algebra of Galois algebras
Let B be a Galois algebra with Galois group G, Jg={b∈B|bx=g(x)b for all x∈B} for each g∈G, and BJg=Beg for a central idempotent eg, Ba the Boolean algebra generated by {0,eg|g∈G}, e a nonzero element in Ba, and He={g∈G|eeg=e}. Then, a monomial e is characterized, and the Galois extension Be, generat...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203202210 |
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| _version_ | 1832554811774468096 |
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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 with Galois group G, Jg={b∈B|bx=g(x)b for all x∈B} for each g∈G, and
BJg=Beg for a central idempotent eg, Ba the Boolean algebra generated by {0,eg|g∈G}, e a nonzero
element in Ba, and He={g∈G|eeg=e}. Then, a
monomial e is characterized, and the Galois extension Be,
generated by e with Galois group He, is investigated. |
| format | Article |
| id | doaj-art-ac9b159906be45759e5c471febd86f1d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ac9b159906be45759e5c471febd86f1d2025-02-03T05:50:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-0120031167367910.1155/S0161171203202210The Boolean algebra of Galois algebrasGeorge Szeto0Lianyong Xue1Department of Mathematics, Bradley University, Peoria, IL 61625, USADepartment of Mathematics, Bradley University, Peoria, IL 61625, USALet B be a Galois algebra with Galois group G, Jg={b∈B|bx=g(x)b for all x∈B} for each g∈G, and BJg=Beg for a central idempotent eg, Ba the Boolean algebra generated by {0,eg|g∈G}, e a nonzero element in Ba, and He={g∈G|eeg=e}. Then, a monomial e is characterized, and the Galois extension Be, generated by e with Galois group He, is investigated.http://dx.doi.org/10.1155/S0161171203202210 |
| spellingShingle | George Szeto Lianyong Xue The Boolean algebra of Galois algebras International Journal of Mathematics and Mathematical Sciences |
| title | The Boolean algebra of Galois algebras |
| title_full | The Boolean algebra of Galois algebras |
| title_fullStr | The Boolean algebra of Galois algebras |
| title_full_unstemmed | The Boolean algebra of Galois algebras |
| title_short | The Boolean algebra of Galois algebras |
| title_sort | boolean algebra of galois algebras |
| url | http://dx.doi.org/10.1155/S0161171203202210 |
| work_keys_str_mv | AT georgeszeto thebooleanalgebraofgaloisalgebras AT lianyongxue thebooleanalgebraofgaloisalgebras AT georgeszeto booleanalgebraofgaloisalgebras AT lianyongxue booleanalgebraofgaloisalgebras |