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portada Commutative Algebra: Volume ii (Graduate Texts in Mathematics, 29)
Type
Physical Book
Publisher
Author
Language
English
Pages
416
Format
Paperback
ISBN13
9783662277539
Edition No.
1

Commutative Algebra: Volume ii (Graduate Texts in Mathematics, 29)

Oscar Zariski; Pierre Samuel (Author) · Springer · Paperback

Commutative Algebra: Volume ii (Graduate Texts in Mathematics, 29) - Oscar Zariski; Pierre Samuel

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Synopsis "Commutative Algebra: Volume ii (Graduate Texts in Mathematics, 29)"

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.

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