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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, TX, and Lance W Small, University of California, San Diego, La Jolla, CA
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Collected Works
2001; 1198 pp; hardcover
Volume: 16
ISBN-10: 0-8218-0688-2
ISBN-13: 978-0-8218-0688-3
List Price: US$216
Member Price: US$172.80
Order Code: CWORKS/16
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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

"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

Part 1
General ring theory
  • Amitsur and ring theory
  • A generalization of a theorem on linear differential equations
  • A general theory of radicals. I. Radicals in complete lattices
  • A general theory of radicals. II. Radicals in rings and bicategories
  • A general theory of radicals. III. Applications
  • Algebras over infinite fields
  • Radicals of polynomial rings
  • Invariant submodules of simple rings
  • Derivations in simple rings
  • The radical of field extensions
  • Countably generated division algebras over nondenumerable fields
  • Commutative linear differential operators
  • Rings with a pivotal monomial
  • On the semi-simplicity of group algebras
  • Derived functors in abelian categories
  • Remarks on principal ideal rings
  • Generalized polynomial identities and pivotal monomials
  • Rings with involution
  • Rings of quotients and Morita contexts
  • Nil radicals. Historical notes and some new results
  • On rings of quotients
  • Recognition of matrix rings II
Rings satisfying a polynomial identity
  • Amitsur and PI rings
  • Nil PI-rings
  • An embedding of PI-rings
  • On rings with identities
  • The \(T\)-ideals of the free ring
  • A generalization of Hilbert's Nullstellensatz
  • Groups with representations of bounded degree II
  • Jacobson-rings and Hilbert algebras with polynomial identities
  • Nil semi-groups of rings with a polynomial identity
  • Rational identities and applications to algebra and geometry
  • Prime rings having polynomial identities with arbitrary coefficients
  • Identities in rings with involutions
  • A noncommutative Hilbert basis theorem and subrings of matrices
  • Embeddings in matrix rings
  • Some results on rings with polynomial identities
  • A note on PI-rings
  • On universal embeddings in matrix rings
  • Polynomial identities and Azumaya algebras
  • Polynomial identities
  • Central embeddings in semi-simple rings
  • Polynomials over division rings
  • Prime ideals in PI-rings
  • Finite-dimensional representations of PI algebras
  • GK-dimensions of corners and ideals
  • Contributions of PI theory to Azumaya algebras
  • Finite-dimensional representation of PI algebras, II
  • Algebras over infinite fields, revisited
  • Acknowledgement
Part 2
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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