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Algebraic Number Theory for Beginners
Af: John Stillwell Engelsk Hardback
SPAR
kr 135
Algebraic Number Theory for Beginners
Af: John Stillwell Engelsk Hardback
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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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.
Produktdetaljer
Sprog: Engelsk
Sider: 250
ISBN-13: 9781316518953
Indbinding: Hardback
Udgave:
ISBN-10: 1316518957
Kategori: Algebra
Udg. Dato: 11 aug 2022
Længde: 22mm
Bredde: 158mm
Højde: 236mm
Oplagsdato: 11 aug 2022
Forfatter(e): John Stillwell
Forfatter(e) John Stillwell


Kategori Algebra


Sprog Engelsk


Indbinding Hardback


Sider 250


Udgave


Længde 22mm


Bredde 158mm


Højde 236mm


Udg. Dato 11 aug 2022


Oplagsdato 11 aug 2022

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