Collected Works 2001; 1198 pp; hardcover Volume: 16 ISBN10: 0821806882 ISBN13: 9780821806883 List Price: US$216 Member Price: US$172.80 Order Code: 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 "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 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
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 PIrings
 Identities and generators of matrix rings
 Identities and linear dependence
 On a central identity for matrix rings
 Alternating identities
 PIalgebras and their cocharacters
 The sequence of codimensions of PIalgebras
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
 Noncommutative 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 MalcevNeumann 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
 Finitedimensional subalgebras of division rings
 Acknowledgment
