Algèbre locale, Multiplicités (Broché)

This series reports on new developments in mathematical research and teaching - quickly, informally and at a high level. The type of material considered for publication includes 1. Research monographs 2. Lectures on a new field or presentations of a new angle in a classical field 3. Summer schools and intensive courses on topics of current research. Texts that are out of print but still in demand may also be considered. The timeliness of a manuscript is sometimes more important than its form, which may in such cases be preliminary or tentative. Details of the editorial policy can be found on the inside front-cover of a current volume. We recommend contacting the publisher or the series editors at an early stage of your project. Addresses are given on the inside bock-cover. Manuscripts should be prepared according to Springer-Verlag's standard specifications. Latex style files may be found at ww. springeronline. com [click on < Mathematics >, then on < For Authors > and look for < Macro Packages for books >]. Style files for other TeX-versions, and additional technical instructions, if necessary, are available on request from : Inm@springer.de. This edition reproduces the 2nd corrected printing of the 3rd edition of the now classic notes by Professor Serre, long established as one of the standard introductory texts on local algebra. Referring for background notions to Bourbaki's "Commutative Algebra" (English edition Springer-Verlag 1988), the book focuses on the various dimension theories and theorems on mulitplicities of intersections with the Carton-Eilenberg functor Tor as the central concept. The main results are the decomposition theorems, theorems of Cohen-Seidenberg, the normalisation of rings of polynomials, dimension (in the sense of Krull) and characteristic polynomials (in the sense of Hilbert-Samuel).