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

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

2、deals.........................................181.2JacobsonRings........................................221.3CoordinateRings.......................................26Exercises..................................................292NoetherianandArtinianRing

3、s...........................332.1TheNoetherandArtinPropertyforRingsandModules.....332.2NoetherianRingsandModules...........................38Exercises..................................................403TheZariskiTopology...............................

4、......433.1AffineVarieties.........................................433.2Spectra...............................................463.3NoetherianandIrreducibleSpaces........................48Exercises..................................................524ASumm

5、aryoftheLexicon...............................554.1TrueGeometry:AffineVarieties..........................554.2AbstractGeometry:Spectra.............................56Exercises..................................................58PartIIDimension5KrullDimensi

6、onandTranscendenceDegree..............61Exercises..................................................7056Contents6Localization..............................................73Exercises..................................................807ThePrincipalIdealT

7、heorem.............................857.1Nakayama’sLemmaandthePrincipalIdealTheorem.......857.2TheDimensionofFibers................................91Exercises..................................................978IntegralExtensions........................

8、...............1038.1IntegralClosure........................................1038.2LyingOver,GoingUpandGoingDown...................1098.3NoetherNormalization..................................114Exercises..................................