| 1. | In this case, the degree of the splitting field is 24.
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| 2. | They proved two important theorems : a splitting fields.
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| 3. | The degree of this splitting field is divisible by n and divides n !.
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| 4. | This field is not the splitting field, but contains one ( any ) root.
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| 5. | For a field containing all the roots of a polynomial, see the splitting field.
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| 6. | This field, unique up to a field isomorphism, is called the splitting field of.
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| 7. | Although different choices of factors may lead to different subfield sequences the resulting splitting fields will be isomorphic.
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| 8. | Normal closure that includes the complex cube roots of unity, and so is not a splitting field.
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| 9. | The problem can be dealt with by shifting to field theory and considering the splitting field of a polynomial.
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| 10. | The Brauer Noether theorem gives a characterization of the splitting fields of a central division algebra over a field.
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