Altman, Allen Burchard & Kleiman, Steven Lawrence - A Term of Commutative Algebra

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1、VersionofSeptember3,20126.DirectLimits..................1537.Filtereddirectlimits................1568.TensorProducts.................158ATermof9.Flatness....................15910.Cayley–HamiltonTheorem.............16111.LocalizationofRings...............164CommutativeAlgebra12.

2、LocalizationofModules..............16713.Support....................168ByAllenALTMAN14.Krull–Cohen–SeidenbergTheory...........17115.NoetherNormalization..............174andStevenKLEIMAN16.ChainConditions................17717.AssociatedPrimes................179Contents18.Primary

3、Decomposition..............18019.Length....................183Preface.......................iii20.HilbertFunctions................1851.RingsandIdeals...................121.Dimension...................1882.PrimeIdeals....................622.Completion..................1903.Radic

4、als......................1023.DiscreteValuationRings..............1934.Modules......................1424.DedekindDomains................1975.ExactSequences...................2025.FractionalIdeals.................1996.DirectLimits....................2626.ArbitraryValuationRings.

5、............2007.FilteredDirectLimits.................33References......................2028.TensorProducts...................37Index........................2039.Flatness......................4310.Cayley–HamiltonTheorem...............4911.LocalizationofRings.................551

6、2.LocalizationofModules................6113.Support.....................6614.Krull–Cohen–SeidenbergTheory.............7115.NoetherNormalization................75Appendix:JacobsonRings...............8016.ChainConditions..................8217.AssociatedPrimes..................871

7、8.PrimaryDecomposition................9119.Length......................9720.HilbertFunctions..................101Appendix:Homogeneity................10721.Dimension....................10922.Completion....................11523.DiscreteValuationRings...............12224.DedekindD

8、omains.................12725.FractionalIdeals.........