Commutative Algebra: Volume II

by Oscar Zariski, Pierre Samuel

Overview

This second volume of our treatise on commutative algebra deals largely with three basic topics, which go beyond the more or less classical material of volume I and are on the whole of a more advanced nature and a more recent vintage. These topics are: (a) valuation theory; (b) theory of polynomial and power series rings (including generalizations to graded rings and modules); (c) local algebra. Because most of these topics have either their source or their best motivation in algebraic geom­ etry, the algebro-geometric connections and applications of the purely algebraic material are constantly stressed and abundantly scattered throughout the exposition. Thus, this volume can be used in part as an introduction to some basic concepts and the arithmetic foundations of algebraic geometry. The reader who is not immediately concerned with geometric applications may omit the algebro-geometric material in a first reading (see" Instructions to the reader," page vii), but it is only fair to say that many a reader will find it more instructive to find out immediately what is the geometric motivation behind the purely algebraic material of this volume. The first 8 sections of Chapter VI (including § 5bis) deal directly with properties of places, rather than with those of the valuation associated with a place. These, therefore, are properties of valuations in which the value group of the valuation is not involved.

Product Details

ISBN-13:	9783662277539
Publisher:	Springer Berlin Heidelberg
Publication date:	01/01/1960
Series:	Graduate Texts in Mathematics , #29
Edition description:	Softcover reprint of the original 1st ed. 1960
Pages:	416
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

About the Author

Oscar Zariski (1899–1986) was born in Russia, studied at the Universities of Kiev and Rome, and emigrated to the United States in 1927. He taught at Johns Hopkins, where he became a Professor in 1937. He joined the mathematical faculty at Harvard University in 1947 and taught there until his retirement in 1969. His Collected Papers were published by MIT Press in four volumes.
Pierre Samuel received his PhD from Princeton University in 1947, and another Doctorate degree from the University of Paris in 1949. He taught at the University of Clermont-Ferrand, and later at the University of Paris-Sud. Dover also publishes his Algebraic Theory of Numbers.

Table of Contents

Valuation Theory.- Polynomial and Power Series Rings.- Local Algebra.