Author | Serre, Jean-Pierre. author |
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Title | Local Algebra [electronic resource] / by Jean-Pierre Serre |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000 |
Connect to | http://dx.doi.org/10.1007/978-3-662-04203-8 |
Descript | XIII, 130 p. online resource |
I. Prime Ideals and Localization -- ยง1. Notation and definitions -- ยง2. Nakayamaโs lemma -- ยง3. Localization -- ยง4. Noetherian rings and modules -- ยง5. Spectrum -- ยง6. The noetherian case -- ยง7. Associated prime ideals -- ยง8. 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-Poincarรฉ 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