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. 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.
All Famous Books of this Author :-
Here is list all books/editions avaliable of this author, We recomended you to download all.
1. Basic Algebra I (2E) by Nathan Jacobson
2. Basic Algebra II (2E) by Nathan Jacobson
3. PI Algebras An Introduction by Nathan Jacobson
4. Structure and Representations of Jordan Algebras by Nathan Jacobson
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 :-
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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