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pi-algebras: an introduction, nathan jacobson [pdf] mathschool

PI Algebras An Introduction by Nathan Jacobson

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About this book :-
PI Algebras An Introduction written by Nathan Jacobson
These are lecture notes for a course on ring theory given by the author at Yale, September - December, 1973. The lectures had two main goals: first, to present an improved version of the theory of algebras with po.lynomial ident~y (over a commutative coefficient ring) based on recent results by Formanek and Rowen and second, to present a detailed and complete account of Amitsur's construction of non-crossed product division algebras.
(Nathan Jacobson)

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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Book Contents :-
PI Algebras An Introduction written by Nathan Jacobson cover the following topics.
INTRODUCTION
1. Assumed background
2. Two results on the radical
3. Prime and semi-prime ideals
I.PI -ALGEBRAS
I. Definitions and examples
2. Formal results
3. Kaplansky-Amitsur theorem
4. Theorem of Amitsur and Levitzki
5. Central simple algebras. Converse of Kaplansky-Amitsur theorem
6. Nil ideals in algebras without units
7. Polynomial identities for algebras without units
8. Central polynomials for matrix algebras
9. Generic minimum polynomials and central polynomials for finite dimensional central simple algebras
10. Commutative localization
11. Prime algebras satisfying proper identities
12. PI - Algebras
13. Identities of an algebra. Universal PI - algebras
II. APPLICATIONS TO FINITE DIMENSIONAL ALGEBRAS
I. Extension of isomorphisms. Splitting fields
2. The Brauer group of a field
3. Cyclic algebras. Some constructions
4. Generic matrix algebras
5. Division algebras over iterated Laurent series fields
6. Non-crossed product division algebras
7. Another result on UD(K,n), K an infinite field
References

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