| 1. | So it is a quasi-excellent catenary local ring that is not excellent.
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| 2. | Local rings also don't have such idempotents, but for a different reason.
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| 3. | A local ring announcer was used instead of the usual Bruce Buffer.
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| 4. | Suppose that " R " is a complete Noetherian local ring.
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| 5. | Then R is a finite local ring which is " not " principal.
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| 6. | This includes the cases of local rings and finite dimensional algebras over fields.
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| 7. | In particular, it is a regular local ring of dimension " n ".
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| 8. | The quotient scheme is the spectrum of a local ring of finite rank.
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| 9. | The local ring in question is then the carrier of the formal moduli.
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| 10. | The local ring at any point is the corresponding valuation ring.
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