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A. Adrian Albert Collected Mathematical Papers
Edited by: Richard E. Block, Nathan Jacobson, J. Marshall Osborn, David J. Saltman, and Daniel Zelinsky

Collected Works
1993; 1840 pp; hardcover
Volume: 3
ISBN-10: 0-8218-0003-5
ISBN-13: 978-0-8218-0003-4
List Price: US$245
Member Price: US$196
Order Code: CWORKS/3
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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.


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, 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 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
  • 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
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