| Commutative Algebra: Volume II Softcover Repri Edition Contributor(s): Zariski, Oscar (Author), Samuel, Pierre (Author) |
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ISBN: 3662277530 ISBN-13: 9783662277539 Publisher: Springer OUR PRICE: $94.05 Product Type: Paperback Published: January 1960 |
| Additional Information |
| BISAC Categories: - Mathematics | Algebra - Abstract - Mathematics | Algebra - General |
| Dewey: 512.44 |
| Series: Graduate Texts in Mathematics |
| Physical Information: 0.87" H x 6.14" W x 9.21" (1.32 lbs) 416 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |