Finite extensions of "'Q "'are also called algebraic number fields and are important in number theory.
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In geometry, a source of confusion is the assumption that a finite extension is infinitely divisible or contains an infinite number of parts.
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Where \ mathcal { O } is the ring of integers in a finite extension of \ mathbb { Q } _ \ ell.
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The Galois group of every finite extension of a finite field is finite and cyclic, with an iterate of the Frobenius endomorphism as its generator.
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The integral closure of a Dedekind domain in a finite extension of the field of fractions is a Dedekind domain; in particular, a noetherian ring.
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*PM : module-finite extensions are integral, id = 9308 new !-- WP guess : module-finite extensions are integral-- Status:
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*PM : module-finite extensions are integral, id = 9308 new !-- WP guess : module-finite extensions are integral-- Status:
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Depending on whether the degree is finite or infinite the extension is called a "'finite extension "'or "'infinite extension " '.
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However, because the Frobenius automorphism is a generator of the Galois group of every finite extension of, it is a generator of every finite quotient of the absolute Galois group.
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The future of the interior either ends after a finite extension, or has a boundary which is eventually generated by new light rays which cannot be traced back to the original sphere.
