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Algebraic number theory for beginnersfollowing a path from Euclid to Noether /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Algebraic number theory for beginnersJohn Stillwell.
其他題名:	following a path from Euclid to Noether /
作者:	Stillwell, John.
出版者:	Cambridge :Cambridge University Press,2022.
面頁冊數:	xiv, 227 p. :ill., digital ;23 cm.
附註:	Title from publisher's bibliographic system (viewed on 01 Aug 2022).
標題:	Algebraic number theory.
電子資源:	https://doi.org/10.1017/9781009004138
ISBN:	9781009004138

Algebraic number theory for beginnersfollowing a path from Euclid to Noether /
Stillwell, John.

Algebraic number theory for beginnersfollowing a path from Euclid to Noether /[electronic resource] :John Stillwell. - Cambridge :Cambridge University Press,2022. - xiv, 227 p. :ill., digital ;23 cm.

Title from publisher's bibliographic system (viewed on 01 Aug 2022).

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.

ISBN: 9781009004138Subjects--Topical Terms:

190879
Algebraic number theory.

LC Class. No.: QA247 / .S85 2022

Dewey Class. No.: 512.74

Algebraic number theory for beginnersfollowing a path from Euclid to Noether /
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500 $a Title from publisher's bibliographic system (viewed on 01 Aug 2022).
520 $a 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.
650 0 $a Algebraic number theory. $3 190879
856 4 0 $u https://doi.org/10.1017/9781009004138