tailieunhanh - An Algebraic Introduction to Complex Projective Geometry

Commutative algebra is the theory of commutative rings and their modules. Although it is an interesting theory in itself, it is generally seen as a tool for geometry and number theory. This is my point of view. In this book I try to organize and present a cohesive set of methods in commutative algebra, for use in geometry. As indicated in the title, I maintain throughout the text a view towards complex projective geometry. In many recent algebraic geometry books, commutative algebra is often treated as a poor relation. One occasionally refers to it, but only reluctantly. It also suffers from having attracted too much attention thirty years. | Cambridge studies in advanced mathematics 47 An Algebraic Introduction to Complex Projective Geometry I. Commutative algebra I An Algebraic Introduction to Complex Projective Geometry 1. Commutative algebra Christian Peskine Professor at University Paris VI Pierre et Marie Curie 1 Cambridge UNIVERSITY PRESS Published by the Press Syndicate of the University of Cambridge The Pitt Building. Trumpington street. Cambridge CB2 1RP 40 West 20th street. New York. NY 10011-4211. USA 10 Stamford Road. Melbourne. Victoria 3166. Australia Cambridge University Press 1996 First published 1996 Printed in Great Britain at the University Press. Cambridge Library of Congress cataloguing ai publication data available A catalogue record for this book is available franthe British Library ISBN 0 521 48072 8 hardback TAG Contents 1 Rings homomorphisms ideals 1 Ideals. Quotient rings. 2 Operations on ideals . 6 Prime ideals and maximal ideals. 7 Nilradicals and Jacobson radicals .10 Comaximal ideals. 11 Unique factorization domains UFDs .12 Exercises. 14 2 Modules 17 Submodules. Homomorphisms. Quotient modules. 18 Products and direct sums . 20 Operations on the submodules of a Freemodules . 22 Homomorphism modules. 24 Finitely generated modules. 25 Exercises. 28 3 Noetherian rings and modules 29 Noetherian rings . 29 Noetherian UFDs. 31 Primary decomposition in Noetherian Radical cf an ideal in a Noetherian Back to primary decomposition in Noetherian Minimal prime ideals. 35 Noetherian modules. 36 Exercises. 37 4 Artinian rings and modules 39 Artinian rings. 39 Artinian modules. 43 Exercises. 43

• Y học thường thức
• homomorphisms
• Modules
• Artinian rings
• Jacobson rings
• Zariski’s main theorem
• Morphisms of affine schemes