Lectures in Abstract Algebra, Volume III: Theory of Fields and Galois Theory by Nathan Jacobson
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About this book :-
Lectures in Abstract Algebra, Volume III: Theory of Fields and Galois Theory written by
Nathan Jacobson
The present volume is the second in the author's series of three dealing with abstract algebra. For an understanding of this volume a certain familiarity with the basic concepts treated in Volume I: groups, rings, fields, homomorphisms, is presupposed. However, we have tried to make this account of linear algebra independent of a detailed knowledge of our first volume. References to specific results are given occasionally but some of the fundamental concepts needed have been treated again. In short, it is hoped that this volume can be read with complete understanding by any student who is mathematically sufficiently mature and who has a familiarity with the standard notions of modern algebra. Our point of view in the present volume is basically the abstract conceptual one. However, from time to time we have deviated somewhat from this. Occasionally formal calculational methods yield sharper results. Moreover, the results of linear algebra are not an end in themselves but are essential tools for use in other branches of mathematics and its applications. It is therefore useful to have at hand methods which are constructive and which can be applied in numerical problems. These methods sometimes necessitate a somewhat lengthier discussion but we have felt that their presentation is justified on the grounds indicated. A student well versed in abstract algebra will undoubtedly observe short cuts. Some of these have been indicated in footnotes. We have included a large number of exercises in the text.
Many of these are simple numerical illustrations of the theory. Others should be difficult enough to test the better students. At any rate a diligent study of these is essential for a thorough understanding of the text.
At various stages in the writing of this book I have benefited from the advice and criticism of many friends. Thanks are particularly due to A. H. Clifford, to G. Hochschild, and to I. Kaplansky for suggestions on earlier versions of the text. Also I am greatly indebted to W. H. Mills, Jr. for painstaking help with the proofs and for last minute suggestions for improvements of the text.
(Nathan Jacobson)
Book Detail :-
Title: Lectures in Abstract Algebra, Volume III: Theory of Fields and Galois Theory
Edition:
Author(s): Nathan Jacobson
Publisher: Springer
Series: Graduate Texts in Mathematics
Year: 1976
Pages: 333
Type: PDF
Language: English
ISBN: 0387901817,9780387901817
Country: US
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About Author :-
Author Nathan Jacobson (1910–1999) was an American mathematician. Nachman Arbiser in Warsaw, Jacobson emigrated to America with his family in 1918. Recognized as one of the leading algebraists of his generation, he wrote more than a dozen standard textbooks. He graduated from the University of Alabama in 1930 and was awarded a doctorate in mathematics from Princeton University in 1934. While working on his thesis, Non-commutative polynomials and cyclic algebras, he was advised by Joseph Wedderburn. Jacobson taught and researched at Bryn Mawr College (1935–1936), the University of Chicago (1936–1937), the University of North Carolina at Chapel Hill (1937–1943), and Johns Hopkins University (1943–1947) before joining Yale University in 1947. He remained at Yale until his retirement.
Nathan Jacobson is from Yale University, Department of Mathematics, New Haven Connecticut.
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1. Basic Algebra I (2E) by Nathan Jacobson
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5. Lectures On Quadratic Jordan Algebras by Nathan Jacobson
6. Lie Algebras by Nathan Jacobson
7. Lectures in Abstract Algebra: II. Linear Algebra by Nathan Jacobson
8. Lectures in Abstract Algebra, Volume III: Theory of Fields and Galois Theory by Nathan Jacobson
9. The Theory of Rings by Nathan Jacobson
10. Finite Dimensional Division Algebras by Nathan Jacobson
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Book Contents :-
Lectures in Abstract Algebra, Volume III: Theory of Fields and Galois Theory written by
Nathan Jacobson
cover the following topics.
1. Finite Dimensional Extension Fields
2. Galois Theory of Equations
3. Abelian Extensions
4. Structure Theory of Fields
5. Valuation Theory
6. Artin Schreier Theory
Index
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