Collected Works 2001; 583 pp; hardcover Volume: 16 ISBN10: 0821829246 ISBN13: 9780821829240 List Price: US$125 Member Price: US$100 Order Code: CWORKS/16.1
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 wideranging 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 "Although written during half a century, even now the papers in the two volumes are a delight to read, combining brilliant new ideas with fresh insights into the work of others."  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 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 semisimplicity 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 PIrings
 An embedding of PIrings
 On rings with identities
 The \(T\)ideals of the free ring
 A generalization of Hilbert's Nullstellensatz
 Groups with representations of bounded degree II
 Jacobsonrings and Hilbert algebras with polynomial identities
 Nil semigroups 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 PIrings
 On universal embeddings in matrix rings
 Polynomial identities and Azumaya algebras
 Polynomial identities
 Central embeddings in semisimple rings
 Polynomials over division rings
 Prime ideals in PIrings
 Finitedimensional representations of PI algebras
 GKdimensions of corners and ideals
 Contributions of PI theory to Azumaya algebras
 Finitedimensional representation of PI algebras, II
 Algebras over infinite fields, revisited
 Acknowledgement
