Algebraic number theory for beginners: following a path from Euclid to Noether
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...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2022
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| Schlagworte: | |
| Online-Zugang: | BSB01 BTU01 FHN01 UBG01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 01 Aug 2022) |
| Beschreibung: | 1 Online-Ressource (xiv, 227 Seiten) |
| ISBN: | 9781009004138 |
| DOI: | 10.1017/9781009004138 |
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-sort | 3512.74 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| doi_str_mv | 10.1017/9781009004138 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
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| institution | BVB |
| isbn | 9781009004138 |
| language | English |
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| spelling | Stillwell, John 1942- (DE-588)128427264 aut Algebraic number theory for beginners following a path from Euclid to Noether John Stillwell Cambridge Cambridge University Press 2022 1 Online-Ressource (xiv, 227 Seiten) txt rdacontent c rdamedia cr rdacarrier 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 Algebraic number theory Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 s DE-604 Erscheint auch als Druck-Ausgabe 978-1-31-651895-3 https://doi.org/10.1017/9781009004138 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Stillwell, John 1942- Algebraic number theory for beginners following a path from Euclid to Noether Algebraic number theory Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| subject_GND | (DE-588)4001170-7 |
| title | Algebraic number theory for beginners following a path from Euclid to Noether |
| title_auth | Algebraic number theory for beginners following a path from Euclid to Noether |
| title_exact_search | Algebraic number theory for beginners following a path from Euclid to Noether |
| title_exact_search_txtP | Algebraic number theory for beginners following a path from Euclid to Noether |
| title_full | Algebraic number theory for beginners following a path from Euclid to Noether John Stillwell |
| title_fullStr | Algebraic number theory for beginners following a path from Euclid to Noether John Stillwell |
| title_full_unstemmed | Algebraic number theory for beginners following a path from Euclid to Noether John Stillwell |
| title_short | Algebraic number theory for beginners |
| title_sort | algebraic number theory for beginners following a path from euclid to noether |
| title_sub | following a path from Euclid to Noether |
| topic | Algebraic number theory Algebraische Zahlentheorie (DE-588)4001170-7 gnd |
| topic_facet | Algebraic number theory Algebraische Zahlentheorie |
| url | https://doi.org/10.1017/9781009004138 |
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