Commutative Algebra: Volume II: 29 (Graduate Texts in Mathematics, 29) - Softcover

Zariski, Oscar; Samuel, Pierre

Softcover

ISBN 10: 3662277530 ISBN 13: 9783662277539

Publisher: Springer, 1960

Synopsis

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 through­ out the exposition. Thus, this volume can be used in part as an introduc­ tion 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.

Edition details

• Publisher: Springer
• Publication date: 1960
• Language: English
• ISBN 10: 3662277530
• ISBN 13: 9783662277539
• Binding: Paperback
• Number of pages: 426