Commutative Algebra: Volume II

di Oscar Zariski (Autore)

Pierre Samuel (Autore)

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 1960

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.

• Autore: Oscar Zariski, Pierre Samuel
• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Collana: Graduate Texts in Mathematics
• Anno: 1960
• Rilegatura: Paperback / softback
• Pagine: 416 p.
• Dimensioni: 235 x 155 mm
• EAN: 9783662277539

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