Items related to Commutative Algebra: Volume II (Dover Books on Mathematics)
Synopsis
The second text in this two-book series extends the classical material of Volume I, which focuses on field theory and the ideal theory of Noetherian rings and Dedekind domains. The connection of Volume II's material to algebraic geometry is stressed throughout the presentation, making this book a practical introduction to some basic concepts and the arithmetical foundations of algebraic geometry.
The opening chapter deals with properties of places and is followed by a chapter that explores the classical properties of polynomial and power series rings and their applications to algebraic geometry. The final chapter examines the theory of local rings, which provides the algebraic basis for the local study of algebraic and analytical varieties. Several helpful Appendixes conclude the text.
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About the Author
Oscar Zariski (1899–1986) was born in Russia, studied at the Universities of Kiev and Rome, and emigrated to the United States in 1927. He taught at Johns Hopkins, where he became a Professor in 1937. He joined the mathematical faculty at Harvard University in 1947 and taught there until his retirement in 1969. His Collected Papers were published by MIT Press in four volumes.
Pierre Samuel received his PhD from Princeton University in 1947, and another Doctorate degree from the University of Paris in 1949. He taught at the University of Clermont-Ferrand, and later at the University of Paris-Sud. Dover also publishes his Algebraic Theory of Numbers.
"About this title" may belong to another edition of this title.
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Commutative Algebra Volume II
Published by
Dover Publications Inc., 2019
ISBN 10: 0486838609
ISBN 13: 9780486838601
Used
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Seller: World of Books (was SecondSale), Montgomery, IL, U.S.A.
Seller rating 5 out of 5 stars
Paperback. Condition: Very Good. 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. Seller Inventory # 00107446261
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Commutative Algebra: Volume II Format: Paperback
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Commutative Algebra Volume II
Published by
Dover Publications Inc., 2019
ISBN 10: 0486838609
ISBN 13: 9780486838601
Used
Paperback
Seller: World of Books Inc, Montgomery, IL, U.S.A.
Seller rating 4 out of 5 stars
Paperback. Condition: Very Good. 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. Seller Inventory # CIN0486838609VG
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COMMUTATIVE ALGEBRA: VOLUME II
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Dover Publications, Incorporated, 2019
ISBN 10: 0486838609
ISBN 13: 9780486838601
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Commutative Algebra Volume II: 2 (Dover Books on Mathematics)
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Commutative Algebra: Vol 2
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Paperback. Condition: Brand New. 414 pages. 9.25x6.25x0.75 inches. In Stock. Seller Inventory # 0486838609
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