Common Inessential Discriminant Divisors
Scenes from the Early History of Algebraic Number Theory
Seiten
2025
American Mathematical Society (Verlag)
978-1-4704-7524-6 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-7524-6 (ISBN)
Mathematical challenges spurred nineteenth-century experts to rethink algebraic number theory when inessential discriminant divisors impeded conventional methods. Annotated key papers showcase how Dedekind, Kronecker, and Hensel turned obstacles into catalysts, reshaping the discipline with fresh insights.
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.
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.
Fernando Q. Gouvea, Colby College, Waterville, ME. Jonathan Webster, Butler University, Indianapolis, IN.
Setting the stage
An outlines of the problem
Dedekind's $/textit{Anzeige}$, 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
Bibliography
Index
| Erscheinungsdatum | 27.11.2025 |
|---|---|
| Reihe/Serie | History of Mathematics |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| ISBN-10 | 1-4704-7524-3 / 1470475243 |
| ISBN-13 | 978-1-4704-7524-6 / 9781470475246 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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