Local Algebra

AvJean-Pierre Serre

Inbunden, Engelska, 2000

Del i serien Springer Monographs in Mathematics

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Beskrivning

This is an English translation of the now classic "Algebre Locale - Multiplicites" originally published by Springer as LNM 11, in several editions since 1965. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities ("Tor-formula"). Many modifications to the original French text have been made by the author for this English edition: they make the text easier to read, without changing its intended informal character.

Produktinformation

Utgivningsdatum:2000-06-16
Mått:155 x 235 x undefined mm
Format:Inbunden
Språk:Engelska
Serie:Springer Monographs in Mathematics
Antal sidor:130
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540666417
Översättare:Chin, C.W., Chin, C. W.

Utforska kategorier

Matematik inom Naturvetenskap och teknik
Algebra inom Naturvetenskap och teknik

Innehållsförteckning

I. Prime Ideals and Localization.- §1. Notation and definitions.- §2. Nakayama’s lemma.- §3. Localization.- §4. Noetherian rings and modules.- §5. Spectrum.- §6. The noetherian case.- §7. Associated prime ideals.- §8. Primary decompositions.- II. Tools.- A: Filtrations and Gradings.- B: Hilbert-Samuel Polynomials.- III. Dimension Theory.- A: Dimension of Integral Extensions.- B: Dimension in Noetherian Rings.- C: Normal Rings.- D: Polynomial Rings.- IV. Homological Dimension and Depth.- A: The Koszul Complex.- B: Cohen-Macaulay Modules.- C: Homological Dimension and Noetherian Modules.- D: Regular Rings.- Appendix I: Minimal Resolutions.- Appendix II: Positivity of Higher Euler-Poincaré Characteristics.- Appendix III: Graded-polynomial Algebras.- V. Multiplicities.- A: Multiplicity of a Module.- B: Intersection Multiplicity of Two Modules.- C: Connection with Algebraic Geometry.- Index of Notation.