eBook - PDF
Algebraic Number Theory for Beginners
Following a Path From Euclid to Noether
- 244 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
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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Information
Table of contents
- Cover
- Half-title
- Title page
- Copyright information
- Dedication
- Contents
- Preface
- Acknowledgments
- 1 Euclidean Arithmetic
- 2 Diophantine Arithmetic
- 3 Quadratic Forms
- 4 Rings and Fields
- 5 Ideals
- 6 Vector Spaces
- 7 Determinant Theory
- 8 Modules
- 9 Ideals and Prime Factorization
- References
- Index
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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 1.5 million books available in our catalogue for you to explore.