This book contains the collected works of A. Adrian Albert, a leading algebraist of the twentieth century. Albert made many important contributions to the theory of the Brauer group and central simple algebras, Riemann matrices, nonassociative algebras, and other topics. Part 1 focuses on associative algebras and Riemann matrices, and Part 2 on nonassociative algebras and miscellany. Because much of Albert's work remains of vital interest in contemporary research, this volume will interest mathematicians in a variety of areas.
Preface Bibliography Professional Biography of A(braham) Adrian Albert Ph.D. students of A. Adrian Albert A. A. Albert by Daniel Zelinsky Abraham Adrian Albert, 1905-1972 by Nathan Jacobson Abraham Adrian Albert, A biographical memoir by Irving Kaplansky A. Adrian Albert by Israel N. Herstein, Collection of articles dedicated to the memory of Abraham Adrian Albert Part 1: A determination of all normal division algebras in sixteen units: On the rank equation of any normal division algebra The rank function of any simple algebra On the structure of normal division algebras Normal division algebras in $4p^2$ units, $p$ an odd prime The structure of any algebra which is a direct product of rational generalized quaternion division algebras The non-existence of pure Riemann matrices with normal multiplication algebras of order sixteen A necessary and sufficient condition for the non-equivalence of any two rational generalized quaternion division algebras Determination of all normal division algebras in thirty-six units of type $R 2$ A note on an important theorem on normal division algebras New results in the theory of normal division algebras A construction of all non-commutative rational division algebras of order eight The structure of pure Riemann matrices with non-commutative multiplication algebras On direct products, cyclic division algebras, and pure Riemann matrices On normal division algebras of type $R$ in thirty-six units On the Wedderburn norm condition for cyclic algebras A note on cyclic algebras of order sixteen On direct products Division algebras over an algebraic field The structure of matrices with any normal division algebra of multiplications On the construction of cyclic algebras with a given exponent Algebras of degree $2^e$ and pure Riemann matrices A construction of non-cyclic normal division algebras Normal division algebras of degree four over an algebraic field On normal simple algebras A note on normal division algebras of order sixteen (with H. Hasse), A determination of all normal division algebras over an algebraic number field A note on the equivalence of algebras of degree two On primary normal division algebras of degree eight Non-cyclic algebras of degree and exponent four Normal division algebras over algebraic number fields not of finite degree Cyclic fields of degree eight On the construction of Riemann matrices I Normal division algebras of degree $4$ over $F$ of characteristic $2$ On certain imprimitive fields of degree $p^2$ over $P$ of characteristic $p$ Normal division algebras over a modular field A solution of the principal problem in the theory of Riemann matrices Cyclic fields of degree $p^n$ over $F$ of characteristic $p$ On normal Kummer fields over a non-modular field The principal matrices of a Riemann matrix A note on the Poincare theorem on impure Riemann matrices On the construction of Riemann matrices II On cyclic fields Involutorial simple algebras and real Riemann matrices Normal division algebras of degree $p^e$ over $F$ of characteristic $p$ Simple algebras of degree $p^e$ over a centrum of characteristic $p$ $p$-algebras over a field generated by one indeterminate Non-cyclic algebras with pure maximal subfields On cyclic algebras A note on normal division algebras of prime degree On ordered algebras On $p$-adic fields and rational division algebras Division algebras over a function field Two element generation of a separable algebra Absolute valued real algebras Absolute-valued algebraic algebras Leonard Eugene Dickson (1874-1954) On involutorial algebras A property of ordered rings On involutorial associative division algebras A normal form for Riemann matrices New results on associative division algebras On associative division algebras (Retiring Presidential Address) A note on certain cyclic algebras Tensor products of quaternion algebras Acknowledgments Part 2: The integers of normal quartic fields: A determination of the integers of all cubic fields The integers represented by sets of ternary quadratic forms On universal sets of positive ternary quadratic forms A note on the Dickson theorem on universal ternaries On a certain algebra of quantum mechanics Integral domains of rational generalized quaternion algebras A note on matrices defining total real fields Normalized integral bases of algebraic number fields I A quadratic form; problem in the calculus of variations Symmetric and alternate matrices in an arbitrary field, I Quadratic null forms over a function field A rule for computing the inverse of a matrix Quadratic forms permitting composition Non-associative algebras. I. Fundamental concepts and isotopy Non-associative algebras. II. New simple algebras The radical of a non-associative algebra An inductive proof of Descartes' rule of signs Quasigroups. I Algebras derived by non-associative matrix multiplication The matrices of factor analysis The minimum rank of a correlation matrix Quasigroups. II Quasiquaternion algebras On Jordan algebras of linear transformations The Wedderburn principal theorem for Jordan algebras A structure theory for Jordan algebras On the power-associativity of rings Power-associative rings On right alternative algebras A theory of trace-admissible algebras Almost alternative algebras A note on the exceptional Jordan algebra A theory of power-associative commutative algebras New simple power-associative algebras Power-associative algebras On nonassociative division algebras On simple alternative rings On commutative power-associative algebras of degree two Rational normal matrices satisfying the incidence equation The structure of right alternative algebras (with M. S. Frank), Simple Lie algebras of characteristic p On Hermitian operators over the Cayley algebra A property of special Jordan algebras On certain trinomial equations in finite fields (with B. Muckenhoupt), On matrices of trace zero On partially stable algebras (with N. Jacobson), On reduced exceptional simple Jordan algebras Addendum to the paper on partially stable algebras A construction of exceptional Jordan division algebras On the orthogonal equivalence of sets of real symmetric matrices A solvable exceptional Jordan algebra (with L. J. Paige), On a homomorphism property of certain Jordan algebras (with John Thompson), Two-element generation of the projective unimodular group Finite noncommutative division algebras Finite division algebras and finite planes On the collineation groups associated with twisted fields On the collineation groups of certain non-Desarguesian planes Generalized twisted fields Isotopy for generalized twisted fields On the nuclei of a simple Jordan algebra On exceptional Jordan division algebras On some properties of biabelian fields On certain polynomial systems Unpublished Articles: Some mathematical aspects of cryptography (with L. J. Paige) Malcev algebras Acknowledgments.