文档介绍：'
An Algebraic Introduction to Vt
Complex Projective Geometry
1. Commutative algebra
Christian Peskine
Professor at University Paris VI, Pierre et Marie Curie
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 Contents
First published 1996
Printed in Great Britain at the University Press. Cambridge
Library of Congress cataloguing an publication data available
1 Rings. homomorphisms. ideals 1
A catalogue record for this book is available from the British Library Ideals . Quotient rings ........................ 2
Operations on ideals ........................ 6
Prime ideals and maximal ideals .................. 7
ISBN 0 521 48072 8 hardback Nilradicals and Jacobson radicals ................. 10
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 module ............ 21
Freemodules ............................ 22
Homomorphism modules ...................... 24
Finitely generated modules ..................... 25
Exercises ............................... 28
3 Noetherian rings and modules 29
Noetherian rings .......................... 29
Noetherian UFDs .......................... 31
Primary position in Noetherian rings ............ 32
Radical of an ideal in a Noetherian ring .............. 33
Back to primary position in Noetherian rings ....... 34
Minimal prime ideals ........................ 35
Noetherian modul