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basic algebra II 2nd edition nathan jacobson [pdf] MathSchool

Basic Algebra II (2E) by Nathan Jacobson

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About this book :-
Basic Algebra II (2E) written by Nathan Jacobson
Basic Algebra 2 is a text for a second course in algebra that presupposes an introductory course covering the type of material contained in the Introduction and the first three or four chapters of Basic Algebra I. These chapters dealt with the rudiments of set theory, group theory, rings, modules, especially modules over a principal ideal domain, and Galois theory focused on the classical problems of solvability of equations by radicals and constructions with straight-edge and compass.
Nathan Jacobson Basic Algebra 2 contains a good deal more material than can be covered in a year's course. Selection of chapters as well as setting limits within chapters will be essential in designing a realistic program for a year.
Volume II comprises all of the subjects usually covered in a first-year graduate course in algebra. Topics include categories, universal algebra, modules, basic structure theory of rings, classical representation theory of finite groups, elements of homological algebra with applications, commutative ideal theory, and formally real fields. In addition to the immediate introduction and constant use of categories and functors, it revisits many topics from Volume I with greater depth and sophistication. Exercises appear throughout the text, along with insightful, carefully explained proofs.

Book Detail :-
Title: Basic Algebra II
Edition: Second Edition
Author(s): Nathan Jacobson
Publisher: Dover Publications
Series:
Year: 2009
Pages: 703
Type: PDF
Language: English
ISBN: 048647187X,9780716719335,9780486471877,0716719339
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 University until his retirement.
He was a member of the National Academy of Sciences and the American Academy of Arts and Sciences. He served as president of the American Mathematical Society from 1971 to 1973, and was awarded their highest honour, the Leroy P. Steele prize for lifetime achievement, in 1998. He was also vice-president of the International Mathematical Union from 1972 to 1974. Nathan Jacobson is Director of , Educational Technology, MAN FACTORS, INC, San Diego, California

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Book Contents :-
Basic Algebra II (2E) written by Nathan Jacobson cover the following topics.
Preface
Preface to the First Edition
0. INTRODUCTION
1. CATEGORIES
2. UNIVERSAL ALGEBRA
3. MODULES
4. BASIC STRUCTURE THEORY OF RINGS
5. CLASSICAL REPRESENTATION THEORY OF FINITE GROUPS
6. ELEMENTS OF HOMOLOGICAL ALGEBRA WITH APPLICATIONS
7. COMMUTATIVE IDEAL THEORY: GENERAL THEORY AND NOETHERIAN RINGS
8. FIELD THEORY
9. VALUATION THEORY
10. DEDEKIND DOMAINS
11. FORMALLY REAL FIELDS
References
Index

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