Episodes in the History of Modern Algebra, (1800-1950)

by Gray, Jeremy J.; Parshall, Karen Hunger

• ISBN13: 9780821843437
• ISBN10: 0821843435
• Format: Hardcover
• Copyright: 2007-08-08
• Publisher: Amer Mathematical Society

Summary

Acknowledgments by J. J. Gray and K. H. Parshall Introduction by J. J. Gray and K. H. Parshall Babbage and French Ideologie: Functional equations, language, and the analytical method by E. L. Ortiz ''Very full of symbols'': Duncan F. Gregory, the calculus of operations, and the Cambridge Mathematical Journal by S. E. Despeaux Divisibility theories in the early history of commutative algebra and the foundations of algebraic geometry by O. Neumann Kronecker's fundamental theorem of general arithmetic by H. M. Edwards Developments in the theory of algebras over number fields: A new foundation for the Hasse norm residue symbol and new approaches to both the Artin reciprocity law and class field theory by G. Frei Minkowski, Hensel, and Hasse: On the beginnings of the local-global principle by J. Schwermer Research in algebra at the University of Chicago: Leonard Eugene Dickson and A. Adrian Albert by D. D. Fenster Emmy Noether's 1932 ICM lecture on noncommutative methods in algebraic number theory by C. W. Curtis From Algebra (1895) to Moderne Algebra (1930): Changing conceptions of a discipline--A guided tour using the Jahrbuch uber die Fortschritte der Mathematik by L. Corry A historical sketch of B. L. van der Waerden's work in algebraic geometry: 1926-1946 by N. Schappacher On the arithmetization of algebraic geometry by S. Slembek The rising sea: Grothendieck on simplicity and generality by C. McLarty

Table of Contents

Acknowledgments

Introduction

Babbage and French Ideologie: Functional equations, language, and the analytical method

"Very full of symbols": Duncan F. Gregory, the calculus of operations, and the Cambridge Mathematical Journal

Divisibility theories in the early history of commutative algebra and the foundations of algebraic geometry

Kronecker's fundamental theorem of general arithmetic

Developments in the theory of algebras over number fields: A new foundation for the Hasse norm residue symbol and new approaches to both the Artin reciprocity law and class field theory

Minkowski, Hensel, and Hasse: On the beginnings of the local-global principle

Research in algebra at the University of Chicago: Leonard Eugene Dickson and A. Adrian Albert

Emmy Noether's 1932 ICM lecture on noncommutative methods in algebraic number theory

From Algebra (1895) to Moderne Algebra (1930): Changing conceptions of a discipline–A guided tour using the Jahrbuch uber die Fortschritte der Mathematik

A historical sketch of B. L. van der Waerden's work in algebraic geometry: 1926-1946

On the arithmetization of algebraic geometry

The rising sea: Grothendieck on simplicity and generality

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