Regular local ring: Difference between revisions
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imported>Giovanni Antonio DiMatteo (New page: There are deep connections between algebraic (in fact, scheme-theoretic) notions of smoothness and regularity. ==Definition== Serre's Regularity Criterion states that a [[Noetherian Ring...) |
imported>Giovanni Antonio DiMatteo (→Definition: minor edit) |
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==Definition== | ==Definition== | ||
Serre's Regularity Criterion states that a [[Noetherian Ring|Noetherian]] [[Local Ring|local ring]] is regular if and only if its [[Global Dimension|global dimension]] is finite, in which case it is equal to the [[Krull dimension]] of <math>A</math>. | Serre's Regularity Criterion states that a [[Noetherian Ring|Noetherian]] [[Local Ring|local ring]] <math>A</math> is regular if and only if its [[Global Dimension|global dimension]] is finite, in which case it is equal to the [[Krull dimension]] of <math>A</math>. | ||
Revision as of 21:39, 21 November 2007
There are deep connections between algebraic (in fact, scheme-theoretic) notions of smoothness and regularity.
Definition
Serre's Regularity Criterion states that a Noetherian local ring is regular if and only if its global dimension is finite, in which case it is equal to the Krull dimension of .
