Commutative Algebra: Volume II
Π½ΠΎΠ΅. 2013β―Π³. Β· Graduate Texts in Mathematics ΠΠ½ΠΈΠ³Π° 29 Β· Springer Science & Business Media
Π-ΠΊΠ½ΠΈΠ³Π°
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Π‘ΡΡΠ°Π½ΠΈΡΠΈ
reportΠΡΠ΅Π½ΠΈΡΠ΅ ΠΈ ΡΠ΅ΡΠ΅Π½Π·ΠΈΠΈΡΠ΅ Π½Π΅ ΡΠ΅ ΠΏΠΎΡΠ²ΡΠ΄Π΅Π½ΠΈ Β ΠΠΎΠ·Π½Π°ΡΡΠ΅ ΠΏΠΎΠ²Π΅ΡΠ΅
ΠΠ° Π΅-ΠΊΠ½ΠΈΠ³Π°Π²Π°
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 Β§ 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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ΠΠ° Π΄Π° ΡΠΈΡΠ°ΡΠ΅ Π½Π° ΡΡΠ΅Π΄ΠΈ ΡΠΎ Π΅-ΠΌΠ°ΡΡΠΈΠ»ΠΎ, ΠΊΠ°ΠΊΠΎ ΡΡΠΎ ΡΠ΅ Π΅-ΡΠΈΡΠ°ΡΠΈΡΠ΅ Kobo, ΡΠ΅ ΡΡΠ΅Π±Π° Π΄Π° ΠΏΡΠ΅Π·Π΅ΠΌΠ΅ΡΠ΅ Π΄Π°ΡΠΎΡΠ΅ΠΊΠ° ΠΈ Π΄Π° ΡΠ° ΠΏΡΠ΅ΡΡΠ»ΠΈΡΠ΅ Π½Π° ΡΡΠ΅Π΄ΠΎΡ. Π‘Π»Π΅Π΄Π΅ΡΠ΅ Π³ΠΈ Π΄Π΅ΡΠ°Π»Π½ΠΈΡΠ΅ ΡΠΏΠ°ΡΡΡΠ²Π° Π²ΠΎ Π¦Π΅Π½ΡΠ°ΡΠΎΡ Π·Π° ΠΏΠΎΠΌΠΎΡ Π·Π° ΠΏΡΠ΅ΡΡΠ»Π°ΡΠ΅ Π½Π° Π΄Π°ΡΠΎΡΠ΅ΠΊΠΈΡΠ΅ Π½Π° ΠΏΠΎΠ΄Π΄ΡΠΆΠ°Π½ΠΈ Π΅-ΡΠΈΡΠ°ΡΠΈ.
