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.
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 representation d'algebres centrales simples Construction d'algebres centrales simples sur des corps de caracteristique zero 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 division 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.