Commutative Algebra. Volume I And Ii. (= Reihe: The University Series In Higher Mathematics). Erstausgaben. Zariski, Oscar And Pierre Samuel; Cohen, I. S. (Cooperation Volume I)

Zwei fadengeheftete kaschierte Ganzleineneinbände mit goldgeprägtem Rückentitel, farbig geprägtem Deckeltitel, geprägtem Deckelsignet und Schutzumschlag. Die Umschläge angerändert, teils hinterlegt und am Rücken nachgedunkelt bzw. gebräunt, Schnitte und Papier des ersten Bandes etwas nachgedunkelt, Schnitte und Vorsätze vereinzelt mit winzigen Fleckchen, ansonsten rundum guter Erhaltungszustand. Im ersten Band mit einzelnen beiliegenden Herleitungen bzw. Beweisführungen von Bertram Huppert. "Vol. I: COMMUTATIVE ALGEBRA has undergone intensive development in the past two decades, creating an urgent need for a systematic account. This volume, the first of a two-volume set, investigates the basic elements of the subject and has as its central topics field theory and the ideal theory of noetherian rings and Dedekind domains. The basic definitions and properties of algebraic structures are properly developed in the first chapter. The second covers field theory, including not only Galois theory but also the main properties of separable transcendental extensions. There follow the elementary properties of ideals in arbitrary rings. Chapter IV studies the important case of noetherian rings with the primary decomposition and its applications, including Krull's dimension theory. The final chapter presents a thorough exposition of Dedekind domains, covering the classical ideal theory of such domains, the properties of the discriminant, and the ramification theory of Hilbert. Clearly and precisely written, Commutative Algebra contains a wealth of information, much of which appears for the first time in book form. Here is a self contained presentation requiring but the rudiments of set theory and linear algebra, including matrices and determinants, for comprehension by any reader. Vol II: THIS volume, devoted to valuation theory, polynomial and power series rings, and local algebra, completes the first systematic treatment of commutative algehra since Krull's monograph of 1935. Using as foundation the more or less classical material of Volume I, the present volume deals with topics of commutative algebra which are on the whole of a more advanced nature and a more recent vintage. Because most of these topics have either their source or their best motivation in algebraic geometry, the algebro-geometric connections and applications of the purely algebraic material are constantly stressed. Thus, this volume can also be used as an introduction to the arithmetic foundations of algebraic geometry. While much of the material appears for the first time in book form, there is also a good deal which is new and represents current or unpublished research. Seven appendices treat special topics of current interest. As in the first volume, the development is detailed, almost leisurely. The clarity and thoroughness of the authors' writing are apparent from the reviews of Volume I that appear on the back cover." (Verlagstext) Oscar Zariski, geboren als Ascher Zaritsky, (* 24. April 1899, in Kobryn, Weißrussland; gestorben 4. Juli 1986 in Brookline, Massachusetts, USA) war ein US-amerikanischer Mathematiker, der wichtige Beiträge zur Grundlegung der algebraischen Geometrie leistete. Pierre Samuel (* 12. September 1921 in Paris; gestorben 23. August 2009 in Paris) war ein französischer Mathematiker, der sich unter anderem mit algebraischer Geometrie beschäftigte. (Wikipedia) In englischer Sprache. XI, (I), 329, (3); X, 414 pages. Groß 8° (160 x 235mm)