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| fixed length control field |
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| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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230904b xxu||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781009001922 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
512.74 |
| Item number |
STI |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Stillwell, John |
| 245 ## - TITLE STATEMENT |
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| Title |
Algebraic number theory for beginners : following a path from Euclid to Noether |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Name of publisher, distributor, etc |
Cambridge University Press, |
| Date of publication, distribution, etc |
2022 |
| Place of publication, distribution, etc |
Cambridge : |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xiv, 227 p. ; |
| Other physical details |
ill., |
| Dimensions |
23 cm |
| 365 ## - TRADE PRICE |
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| Price amount |
39.99 |
| Price type code |
GBP |
| Unit of pricing |
110.40 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
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 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Algebra |
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| Topical term or geographic name as entry element |
Number theory |
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| Topical term or geographic name as entry element |
Euclidean arithmetic |
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| Topical term or geographic name as entry element |
Diophantine arithmetic |
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| Topical term or geographic name as entry element |
Quadratic forms |
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| Topical term or geographic name as entry element |
Rings and fields |
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| Topical term or geographic name as entry element |
Vector spaces |
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| Topical term or geographic name as entry element |
Ideals and prime factorization |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
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| Item type |
Books |