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Algebraic Number Theory for Beginners

Algebraic Number Theory for Beginners

Following a Path From Euclid to Noether

John Stillwell

Cambridge University Press
Publication date : 2022-08-11

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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.

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About the book

Author

John Stillwell

Imprint

Cambridge University Press

Collection

n.c

Publication date

2022-08-11

Pages

n.c

Print ISBN

9781316518953

Language

English

Ebook informations

EAN PDF

9781009019224

Price

£32.70

Copy count 0

Print count 0

File size 3973 Ko

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About author(s)

John Stillwell

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