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The following theorem is usually referred to as Kummer theory.
Definition 1 Let $n$ be a positive integer and let $K$ be a field of characteristic not dividing $n$ which contains the $n$ -th roots of unity. An extension of $K$ of the form: $$K(\sqrt[n]{a_1},\sqrt[n]{a_2},\ldots,\sqrt[n]{a_k})$$ with $a_i \in K^\times$ is called a Kummer extension of $K$ . Notice that the Galois group of the extension is of exponent $n$ .
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"Kummer theory" is owned by alozano.
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Cross-references: Galois group, degree, cyclic extension, extension, roots of unity, contains, characteristic, field, integer, positive, theory, theorem
There are 5 references to this entry.
This is version 2 of Kummer theory, born on 2005-02-22, modified 2005-02-22.
Object id is 6793, canonical name is KummerTheory.
Accessed 4442 times total.
Classification:
| AMS MSC: | 12F05 (Field theory and polynomials :: Field extensions :: Algebraic extensions) |
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Pending Errata and Addenda
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