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:2018-07-28

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

2、....................181.2JacobsonRings........................................221.3CoordinateRings.......................................26Exercises..................................................292NoetherianandArtinianRings...........................332.1TheNoetherandArtinP

3、ropertyforRingsandModules.....332.2NoetherianRingsandModules...........................38Exercises..................................................403TheZariskiTopology.....................................433.1AffineVarieties.........................................433.2Spectra.

4、..............................................463.3NoetherianandIrreducibleSpaces........................48Exercises..................................................524ASummaryoftheLexicon...............................554.1TrueGeometry:AffineVarieties..........................5

5、54.2AbstractGeometry:Spectra.............................56Exercises..................................................58PartIIDimension5KrullDimensionandTranscendenceDegree..............61Exercises..................................................7056Contents6Localization......

6、........................................73Exercises..................................................807ThePrincipalIdealTheorem.............................857.1Nakayama’sLemmaandthePrincipalIdealTheorem.......857.2TheDimensionofFibers................................91Exercise

7、s..................................................978IntegralExtensions.......................................1038.1IntegralClosure........................................1038.2LyingOver,GoingUpandGoingDown...................1098.3NoetherNormalization..........................

8、........114Exercises..................................

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