The second volume of this treatise addresses three basic topics that extend the classical material of Volume I and are of a more advanced nature and recent vintage. These are valuation theory, theory of polynomial and power series rings (including generalizations to graded rings and modules), and local algebra. The connection of this material to algebraic geometry is stressed throughout the presentation.
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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.
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