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

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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..............61Exerc

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

7、aandthePrincipalIdealTheorem.......857.2TheDimensionofFibers................................91Exercises..................................................978IntegralExtensions.......................................1038.1IntegralClosure...........................

8、.............1038.2LyingOver,GoingUpandGoingDown...................1098.3NoetherNormalization..................................114Exercises..................................