Collected Works 1993; 1840 pp; hardcover Volume: 3 ISBN10: 0821800035 ISBN13: 9780821800034 List Price: US$245 Member Price: US$196 Order Code: CWORKS/3
 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. Readership A wide range of mathematicians, physicists, and engineers interested in Albert's work. Table of Contents  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, 19051972 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 nonexistence of pure Riemann matrices with normal multiplication algebras of order sixteen
 A necessary and sufficient condition for the nonequivalence of any two rational generalized quaternion division algebras
 Determination of all normal division algebras in thirtysix 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 noncommutative rational division algebras of order eight
 The structure of pure Riemann matrices with noncommutative multiplication algebras
 On direct products, cyclic division algebras, and pure Riemann matrices
 On normal division algebras of type \(R\) in thirtysix 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 noncyclic 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
 Noncyclic 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 nonmodular field
 The principal matrices of a Riemann matrix
 A note on the Poincaré 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
 Noncyclic 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
 Absolutevalued algebraic algebras
 Leonard Eugene Dickson (18741954)
 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
 Nonassociative algebras. I. Fundamental concepts and isotopy
 Nonassociative algebras. II. New simple algebras
 The radical of a nonassociative algebra
 An inductive proof of Descartes' rule of signs
 Quasigroups. I
 Algebras derived by nonassociative 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 powerassociativity of rings
 Powerassociative rings
 On right alternative algebras
 A theory of traceadmissible algebras
 Almost alternative algebras
 A note on the exceptional Jordan algebra
 A theory of powerassociative commutative algebras
 New simple powerassociative algebras
 Powerassociative algebras
 On nonassociative division algebras
 On simple alternative rings
 On commutative powerassociative 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), Twoelement 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 nonDesarguesian 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
