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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |