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Commutative Algebra : Volume II / by Oscar Zariski, Pierre Samuel.
- Format:
- Book
- Author/Creator:
- Zariski, Oscar, 1899-1986, author.
- Samuel, Pierre, 1921- author.
- Series:
- Graduate texts in mathematics 2197-5612 ; 29.
- Graduate Texts in Mathematics, 2197-5612 ; 29
- Language:
- English
- Subjects (All):
- Commutative algebra.
- Commutative rings.
- Commutative Rings and Algebras.
- Local Subjects:
- Commutative Rings and Algebras.
- Physical Description:
- 1 online resource (X, 416 pages).
- Edition:
- First edition 1960.
- Contained In:
- Springer Nature eBook
- Place of Publication:
- Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1960.
- System Details:
- text file PDF
- Summary:
- 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.
- Contents:
- Valuation Theory
- Polynomial and Power Series Rings
- Local Algebra.
- Other Format:
- Printed edition:
- ISBN:
- 9783662292440
- Access Restriction:
- Restricted for use by site license.
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