Get Algèbre locale, multiplicités PDF

By Jean-Pierre Serre, Pierre Gabriel

ISBN-10: 3540070281

ISBN-13: 9783540070283

This version reproduces the 2d corrected printing of the 3rd version of the now vintage notes by way of Professor Serre, lengthy demonstrated as one of many regular introductory texts on neighborhood algebra. Referring for historical past notions to Bourbaki's "Commutative Algebra" (English variation Springer-Verlag 1988), the ebook focusses at the a number of size theories and theorems on mulitplicities of intersections with the Cartan-Eilenberg functor Tor because the imperative proposal. the most effects are the decomposition theorems, theorems of Cohen-Seidenberg, the normalisation of earrings of polynomials, measurement (in the experience of Krull) and attribute polynomials (in the feel of Hilbert-Samuel).

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Example text

Est polynomial. c) I1 existe un entier r tel que ~ rf soit ROo -@quivalent & 2. , August 1957). Une fonction additive des objets de Si la suite C dans un groupe abglien 0 alors sur )M ~N + ) P TShoku Math. est une application C ~ telle que: ) 0 de C est exacte, 9 De la d~finition on d~duit sans difficult~ les deux propositions suivantes: Si M est un module de une suite de composition de C , et M OCM oC M I .... ~ formge d'objets de C Mn = M , alors i = n i= Si I 0 - - - - ~ M I ----)M 2 ~ exacte de C ) 0 .....

I) de - )(ii). P ceci entra~ne (ii) ~(iii). l'adh@rence P = 0 Si N de z@ro; la topologie )(i). ferm@ dans A Corollaire ~: q n Soit m N A et comme de M , le fait que soit ferm@. P q-adique (lemme de Nakayama). est un sous-module soit s@par@ entraSne que (iii) a_ P est la topologie la moins fine, d'ofl q~r, M/N Soit est local, et si ~ ~ q A . Puisque , d'oG aussi est distinct de m B ~ ~ A =0 Cela r@sulte du corollaire pr@c@dent. On appelle anneau de Zariski un anneau topologique noeth@rien dont la topolo~ie peut Gtre d@finie par les puissances d'un id@al ~ contenu darts le radical de l'anneau.

4)~I): Supposons en effet que associ@ ~ M A/~ , et . Alors N Cor~llaire: N' est associ~ ~ dans M Si p~V(M) 0 = M ~~ M I C . . C M n = ~ module A/p i , ~i N' contient un sous-module M/N' Ann(M) ideal premier contienne contient un sous-module ~/N' et donc que essentiel de p tel que ne rencontre pas contient alors un sous-module I1 en r@sulte que A/p M A - p x~M N isomorphe isomorphe ~ N/N' p~ isomorphe ou est un ideal premier 9 , il existe une suite de composition de telle ~ue ~i+I/Mi M , s 9 soit isomorphe ~ un premier, o~ l'un au moins des ~i est @~al ~ En effet, avec les notations de la d@monstraticn pr~c~dente il suffit de mettre bout & bout une suite de composition de suite de composition de M/N' N' et une qui satisfait aux conditions du Coro~- laire 4 de la proposition 7.

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Algèbre locale, multiplicités by Jean-Pierre Serre, Pierre Gabriel

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