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Algebraic Number Theory For Beginners Following A Path From Euclid To Noether John Stillwell

Name: Algebraic Number Theory For Beginners Following A Path From Euclid To Noether John Stillwell
SKU: BELL-44477458
Price: 31.00 USD
Availability: InStock
Rating: 5 (40 reviews)

SKU: BELL-44477458

$ 31.00 ~~$ 45.00~~ (-31%)

5.0

40 reviews

Algebraic Number Theory For Beginners Following A Path From Euclid To Noether John Stillwell instant download after payment.

Publisher: Cambridge University Press

File Extension: PDF

File size: 3.29 MB

Pages: 243

Author: John Stillwell

ISBN: 9781316518953, 9781009001922, 1316518957, 1009001922

Language: English

Year: 2022

Product desciption

Algebraic Number Theory For Beginners Following A Path From Euclid To Noether John Stillwell by John Stillwell 9781316518953, 9781009001922, 1316518957, 1009001922 instant download after payment.

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.