| 1. | He illustrated the principle with applications in ring theory and field extensions.
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| 2. | Let L / K be a finite field extension of global fields.
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| 3. | The field extension generated by } }, however, is of degree 3.
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| 4. | It suffices to show that "'C "'has no proper finite field extension.
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| 5. | In particular, this applies to finite field extensions of " K ".
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| 6. | Any finite field extension of a finite field is separable and simple.
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| 7. | Classically one is mainly interested in solutions in difference field extensions of K.
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| 8. | A Galois extension is a field extension that is both normal and separable.
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| 9. | These field extensions are also known as algebraic function fields over " K ".
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| 10. | Minimal polynomials are useful for constructing and analyzing field extensions.
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