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Algebraic Number Theory for Beginners

About Algebraic Number Theory for Beginners

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.

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  • Language:
  • English
  • ISBN:
  • 9781316518953
  • Binding:
  • Hardback
  • Pages:
  • 250
  • Published:
  • August 11, 2022
  • Edition:
  • Dimensions:
  • 236x158x22 mm.
  • Weight:
  • 498 g.
Delivery: 2-3 weeks
Expected delivery: October 24, 2024

Description of Algebraic Number Theory for Beginners

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.

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