| 1. | When one takes the ring to be the ring of integers.
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| 2. | In fact, every ideal of the ring of integers is principal.
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| 3. | In some cases, this ring of integers is equivalent to the ring.
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| 4. | The ring is the simplest possible ring of integers.
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| 5. | The ring of integers modulo is a finite field if and only if is prime.
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| 6. | Higher K groups can also be employed and interpreted arithmetically in connection to rings of integers.
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| 7. | For example, this applies to the ring of integers in a p-adic field.
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| 8. | If is the spectrum of the ring of integers, then is the Riemann zeta function.
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| 9. | These special values were known to be related to the etale cohomology of the ring of integers.
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| 10. | On the other hand, the ring of integers in a number field is always a Dedekind domain.
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