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＜電子ブック＞
Local Algebra / by Jean-Pierre Serre
(Springer Monographs in Mathematics. ISSN:21969922)

版	1st ed. 2000.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	2000
本文言語	英語
大きさ	XV, 130 p : online resource
冊子体	Local algebra / Jean-Pierre Serre ; translated from the French by Chee Whye Chin
著者標目	*Serre, Jean-Pierre author SpringerLink (Online service)
件　名	LCSH:Algebra FREE:Algebra
一般注記	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 The present book is an English translation of Algebre Locale - Multiplicites published by Springer-Verlag as no. 11 of the Lecture Notes series. The original text was based on a set of lectures, given at the College de France in 1957-1958, and written up by Pierre Gabriel. Its aim was to give a short account of Commutative Algebra, with emphasis on the following topics: a) Modules (as opposed to Rings, which were thought to be the only subject of Commutative Algebra, before the emergence of sheaf theory in the 1950s); b) H omological methods, a la Cartan-Eilenberg; c) Intersection multiplicities, viewed as Euler-Poincare characteristics. The English translation, done with great care by Chee Whye Chin, differs from the original in the following aspects: - The terminology has been brought up to date (e.g. "cohomological dimension" has been replaced by the now customary "depth"). I have rewritten a few proofs and clarified (or so I hope) a few more. - A section on graded algebras has been added (App. III to Chap. IV). - New references have been given, especially to other books on Commu- tive Algebra: Bourbaki (whose Chap. X has now appeared, after a 40-year wait) , Eisenbud, Matsumura, Roberts, .... I hope that these changes will make the text easier to read, without changing its informal "Lecture Notes" character Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-3-662-04203-8

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