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Selected Papers of S. A. Amitsur with Commentary
Edited by: Avinoam Mann, Hebrew University of Jerusalem, Israel, Amitai Regev, Weizmann Institute of Science, Rehovot, Israel, Louis Rowen, Bar-Ilan University, Ramat-Gan, Israel, David J Saltman, University of Texas, Austin, Texas, and Lance W Small, University of California, San Diego, La Jolla, California
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Collected Works
2001; 615 pp; hardcover
Volume: 16
ISBN-10: 0-8218-2925-4
ISBN-13: 978-0-8218-2925-7
List Price: US$122
Member Price: US$97.60
Order Code: CWORKS/16.2
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This item is also sold as part of the following set: CWORKS/16

A lead figure in twentieth century noncommutative algebra, S. A. Amitsur's contributions are wide-ranging and enduring. This volume collects almost all of his work. The papers are organized into broad topic areas: general ring theory, rings satisfying a polynomial identity, combinatorial polynomial identity theory, and division algebras. Included are essays by the editors on Amitsur's work in these four areas and a biography of Amitsur written by A. Mann. This volume makes a fine addition to any mathematics book collection.

Readership

Graduate students and research mathematicians interested in ring theory, combinatorial algebra, and number theory.

Reviews

"There is no doubt that the collected papers should help and inspire the reader to look at the topic even more deeply."

-- Mathematical Reviews

"These volumes are a collection of short and very readable papers, which many working algebraists will want to own; they should certainly form part of every mathematics library."

-- Zentralblatt MATH

Table of Contents

Combinatoiral polynomial identity theory
  • Amitsur and combinatorial P.I. theory
  • Minimal identities for algebras
  • Remarks on minimal identities for algebras
  • The identities of PI-rings
  • Identities and generators of matrix rings
  • Identities and linear dependence
  • On a central identity for matrix rings
  • Alternating identities
  • PI-algebras and their cocharacters
  • The sequence of codimensions of PI-algebras
Division algebras
  • Amitsur and division algebras
  • Contributions to the theory of central simple algebras
  • La représentation d'algèbres centrales simples
  • Construction d'algèbres centrales simples sur des corps de caractéristique zéro
  • Non-commutative cyclic fields
  • Differential polynomials and division algebras
  • Generic splitting fields of central simple algebras
  • Finite subgroups of division rings
  • Some results on central simple algebras
  • On arithmetic functions
  • Simple algebras and cohomology groups of arbitrary fields
  • Some results on arithmetic functions
  • Finite dimensional central divison algebras
  • Homology groups and double complexes for arbitrary fields
  • On a lemma in elementary proofs of the prime number theorem
  • Complexes of rings
  • On central division algebras
  • The generic division rings
  • Generic abelian crossed products and \(p\)-algebras
  • Division algebras of degree 4 and 8 with involution
  • On the characteristic polynomial of a sum of matrices
  • Generic splitting fields. Brauer groups in ring theory and algebraic geometry.
  • Extension of derivations to central simple algebras
  • Kummer subfields of Malcev-Neumann division algebras
  • Symplectic modules
  • Totally ramified splitting fields of central simple algebras over Henselian fields
  • Galois splitting fields of a universal division algebra
  • Elements of reduced trace 0
  • Finite-dimensional subalgebras of division rings
  • Acknowledgment
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