Algebraic Number Theory for Beginners: Following a Path From Euclid to Noether

Stillwell, John

ISBN 10: 1316518957 / ISBN 13: 9781316518953

Published by Cambridge University Press (edition New), 2022

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Bibliographic Details

• Title: Algebraic Number Theory for Beginners: Following a Path From Euclid to Noether
• Publisher: Cambridge University Press (edition New)
• Publication Date: 2022
• Language: English
• ISBN 10: 1316518957
• ISBN 13: 9781316518953
• Binding: Hardcover
• Edition: New.
• Condition: Very Good

About this title

Synopsis

This book introduces algebraic number theory through the problem of generalizing 'unique prime factorization' from ordinary integers to more general domains. Solving polynomial equations in integers leads naturally to these domains, but unique prime factorization may be lost in the process. To restore it, we need Dedekind's concept of ideals. However, one still needs the supporting concepts of algebraic number field and algebraic integer, and the supporting theory of rings, vector spaces, and modules. It was left to Emmy Noether to encapsulate the properties of rings that make unique prime factorization possible, in what we now call Dedekind rings. The book develops the theory of these concepts, following their history, motivating each conceptual step by pointing to its origins, and focusing on the goal of unique prime factorization with a minimum of distraction or prerequisites. This makes a self-contained easy-to-read book, short enough for a one-semester course.

About the Author

John Stillwell is the author of many books on mathematics; among the best known are Mathematics and its History, Naive Lie Theory, and Elements of Mathematics. He is a member of the inaugural class of Fellows of the American Mathematical Society and winner of the Chauvenet Prize for mathematical exposition.