| 11. | He proved the Cohen structure theorem for complete Noetherian local rings.
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| 12. | The paper showed that a germs of holomorphic functions, local rings, and differential forms.
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| 13. | The dual numbers form a local ring since there is a unique maximal ideal.
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| 14. | The product of the local rings of a commutative ring is a faithfully flat module.
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| 15. | A colorful truck with a loudspeaker announcing a bullfight at a local ring passed by.
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| 16. | Local rings play a major role in valuation theory.
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| 17. | Certain commutative rings can be embedded in local rings via localization at a prime ideal.
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| 18. | In the local ring case, it does matter.
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| 19. | Serre proved this for all regular local rings.
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| 20. | This ring is a 2-dimensional Noetherian regular local ring, and in particular a unique factorization domain.
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