eBook - PDF

Algebraic Number Theory for Beginners

Name: Algebraic Number Theory for Beginners
ISBN: 9781009019224

Following a Path From Euclid to Noether

John Stillwell,

English
PDF
Available on iOS & Android

eBook - PDF

Algebraic Number Theory for Beginners

Following a Path From Euclid to Noether

John Stillwell,

About this book

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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Yes, you can access Algebraic Number Theory for Beginners by John Stillwell in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebra. We have over one million books available in our catalogue for you to explore.