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The Theory of Rings by Nathan Jacobson
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About this book :-
The Theory of Rings written by
The book is mainly concerned with the theory of rings in which both maximal and minimal conditions hold for ideals (except in the last chapter, where rings of the type of a maximal order in an algebra are considered). The central idea consists of representing rings as rings of endomorphisms of an additive group, which can be achieved by means of the regular representation.
The theory that forms the subject of this book had its beginning with Artin's extension in 1927 of Wedderhurn's structure theory· of algebras to rings satisfying the chain conditions. Since then the thc·ory ha~ been ronsiderably extended and sin1plified. rrhe only exposition of the snbjPct in book forn1 that has appeared to date is deuring's Algcbren published in the Ergebnisse series in 1935. Much progress has been nutde since then and this perhaps justifies a new exposition of the suqject.
Book Detail :-
Title: The Theory of Rings
Author(s): Nathan Jacobson
Publisher: American Mathematical Society
Series: Mathematical Surveys and Monographs
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About Author :-
Author Nathan Jacobson (1910 – 1999) was an American mathematician. He was born Warsaw, Congress Poland, Russian Empire and emigrated to America with his family in 1918.
He was graduated from the University of Alabama in 1930 and was awarded a doctorate in mathematics from Princeton University on his thesis Non-commutative polynomials and cyclic algebras in 1934.
Jacobson start his career as teacher at Bryn Mawr College in 1935. He join University of Chicago in 1936 and then University of North Carolina at Chapel Hill in 1937 and Johns Hopkins University in 1943 and at then end Yale University in 1947 until his retirement. He was a member of the National Academy of Sciences and the American Academy of Arts and Sciences. He also 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.
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Book Contents :-
The Theory of Rings written by
cover the following topics.
1. GROUPS AND ENDOMORPHISMS
2. VECTOR SPACEs
3. Non coMMuTATIVE PRINCIPAL IDEAL DoMAINS
4. STRUCTURE OF RINGS OF ENDOl\IORPHISMs AND OF ABsTRACT RINGS
5. A.LGEBRAS OVER A FJELD
6. MuLTIPLICATIVE IDEAL THEORY
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