gtm256.a.course.in.commutative.algebra,.kemper,.gregor,.(2010,.isbn.978-3-642-03544-9)

gtm256.a.course.in.commutative.algebra,.kemper,.gregor,.(2010,.isbn.978-3-642-03544-9)

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时间:2018-08-02

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1、GregorKemperACourseinCommutativeAlgebraMarch31,2009SpringerToIdaleixisandMartinContentsIntroduction..................................................9PartITheAlgebraGeometryLexicon1Hilbert’sNullstellensatz..................................171.1MaximalIdeals......

2、...................................181.2JacobsonRings........................................221.3CoordinateRings.......................................26Exercises..................................................292NoetherianandArtinianRings.....................

3、......332.1TheNoetherandArtinPropertyforRingsandModules.....332.2NoetherianRingsandModules...........................38Exercises..................................................403TheZariskiTopology.....................................433.1AffineVarieties.........

4、................................433.2Spectra...............................................463.3NoetherianandIrreducibleSpaces........................48Exercises..................................................524ASummaryoftheLexicon.............................

5、..554.1TrueGeometry:AffineVarieties..........................554.2AbstractGeometry:Spectra.............................56Exercises..................................................58PartIIDimension5KrullDimensionandTranscendenceDegree..............61Exercises......

6、............................................7056Contents6Localization..............................................73Exercises..................................................807ThePrincipalIdealTheorem.............................857.1Nakayama’sLemmaandthePrinc

7、ipalIdealTheorem.......857.2TheDimensionofFibers................................91Exercises..................................................978IntegralExtensions.......................................1038.1IntegralClosure........................................1

8、038.2LyingOver,GoingUpandGoingDown...................1098.3NoetherNormalization..................................114Exercises..................................

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