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 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.