Common inessential discriminant divisors : scenes from the early history of algebraic number theory / Fernando Q. Gouvêa, Jonathan Webster.

Format:

Book

Author/Creator:

Gouvêa, Fernando Q. (Fernando Quadros), author.

Webster, Jonathan, 1978- author.

Series:

History of mathematics ; v. 47.

History of mathematics. Sources ; vol 47

Language:

English

Subjects (All):

Algebraic number theory--History.

Algebraic number theory.

Number theory.

Physical Description:

1 online resource (xi, 141 pages).

Other Title:

Scenes from the early history of algebraic number theory

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2025]

Summary:

"In mathematics, technical difficulties can spark groundbreaking ideas. This book explores one such challenge: a problem that arose in the formative years of algebraic number theory and played a major role in the early development of the field. When nineteenth-century mathematicians set out to generalize E. E. Kummer's theory of ideal divisors in cyclotomic fields, they discovered that the existence of "common inessential discriminant divisors" blocked the obvious path. Through extensively annotated translations of key papers, this book traces how Richard Dedekind, Leopold Kronecker, and Kurt Hensel approached these divisors, using them to justify the need for entirely new mathematical ideas and to demonstrate their power. Mathematicians interested in algebraic number theory will enjoy seeing what the field, which is still evolving today, looked like in its very early days. Historians of mathematics will find interesting questions for further study. Engaging and carefully researched, Common Inessential Discriminant Divisors is both a historical study and an invitation to experience mathematics as it was first discovered." --Publisher.

Contents:

Setting the stage

An outline of the problem

Dedekind’s Anzeige, 1871

Dedekind on higher congruences

Kronecker on CIDDs

Hensel’s 1894 paper on common inessential discriminant divisors

The rock in the middle of the road.

Notes:

Includes bibliographical references and index.

Online resource; title from PDF title page (AMS, viewed December 18, 2025).

Other Format:

Print version: Gouvêa, Fernando Q. (Fernando Quadros) Common inessential discriminant divisors

ISBN:

1470481812

9781470481810

OCLC:

1545022381

Access Restriction:

Restricted for use by site license