Titolo: Lectures in Abstract Algebra, Part 3: Theory of Fields and Galois Theory (Graduate Texts in Mathematics 32)
Editore: Springer
Data di pubblicazione: 1964
Lingua: Inglese
ISBN 10: 038790168X
ISBN 13: 9780387901688
Rilegatura: Hardcover
Condizione: Good
Condizione della sovraccoperta: No Jacket
Peso: 1,01 libbre

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Riassunto

The present volume completes the series of texts on algebra which the author began more than ten years ago. The account of field theory and Galois theory which we give here is based on the notions and results of general algebra which appear in our first volume and on the more elementary parts of the second volume, dealing with linear algebra. The level of the present work is roughly the same as that of Volume II. In preparing this book we have had a number of objectives in mind. First and foremost has been that of presenting the basic field theory which is essential for an understanding of modern algebraic number theory, ring theory, and algebraic geometry. The parts of the book concerned with this aspect of the subject are Chapters I, IV, and V dealing respectively with finite dimen� sional field extensions and Galois theory, general structure theory of fields, and valuation theory. Also the results of Chapter IlIon abelian extensions, although of a somewhat specialized nature, are ofinterest in number theory. A second objective of our ac� count has been to indicate the links between the present theory of fields and the classical problems which led to its development.

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