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Synopsis
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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À propos de l?auteur
John Stillwell is the author of many books on mathematics; among the best known are Mathematics and its History, Naive Lie Theory, and Elements of Mathematics. He is a member of the inaugural class of Fellows of the American Mathematical Society and winner of the Chauvenet Prize for mathematical exposition.
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Algebraic Number Theory for Beginners: Following a Path From Euclid to Noether
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Cambridge University Press, 2022
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ISBN 13 : 9781316518953
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Algebraic Number Theory for Beginners Algebraic Number Theory for Beginners: Following a Path From Euclid to Noether
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ISBN 10 : 1316518957
ISBN 13 : 9781316518953
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Algebraic Number Theory for Beginners: Following a Path From Euclid to Noether
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ISBN 10 : 1316518957
ISBN 13 : 9781316518953
Neuf
Couverture rigide
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Algebraic Number Theory for Beginners Algebraic Number Theory for Beginners: Following a Path from Euclid to Noether
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ISBN 10 : 1316518957
ISBN 13 : 9781316518953
Neuf
Couverture rigide
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Algebraic Number Theory for Beginners: Following a Path from Euclid to Noether
Edité par
Cambridge University Press, 2022
ISBN 10 : 1316518957
ISBN 13 : 9781316518953
Neuf
Couverture rigide
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Gebunden. Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book, meant for undergraduate mathematics students and teachers, introduces algebraic number theory through problems from ordinary number theory that can be solved with the help of algebraic numbers, using a suitable generalization of unique prime fact. N° de réf. du vendeur 539766801
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Algebraic Number Theory for Beginners: Following a Path From Euclid to Noether
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ISBN 10 : 1316518957
ISBN 13 : 9781316518953
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Algebraic Number Theory for Beginners (Hardcover)
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Hardcover. Etat : new. Hardcover. 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. This book, meant for undergraduate mathematics students and teachers, introduces algebraic number theory through problems from ordinary number theory that can be solved with the help of algebraic numbers, using a suitable generalization of unique prime factorization. The material is motivated by weaving historical information throughout. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. N° de réf. du vendeur 9781316518953
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Algebraic Number Theory for Beginners
Edité par
Cambridge University Press, 2022
ISBN 10 : 1316518957
ISBN 13 : 9781316518953
Neuf
Couverture rigide
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Buch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. N° de réf. du vendeur 9781316518953
Quantité disponible : 1 disponible(s)
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Algebraic Number Theory for Beginners Algebraic Number Theory for Beginners: Following a Path from Euclid to Noether
Edité par
Cambridge University Press, 2022
ISBN 10 : 1316518957
ISBN 13 : 9781316518953
Neuf
Couverture rigide
Vendeur : Revaluation Books, Exeter, Royaume-Uni
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Hardcover. Etat : Brand New. 250 pages. 9.00x6.00x0.56 inches. In Stock. N° de réf. du vendeur x-1316518957
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Algebraic Number Theory for Beginners: Following a Path From Euclid to Noether
Edité par
Cambridge University Press, 2022
ISBN 10 : 1316518957
ISBN 13 : 9781316518953
Neuf
Couverture rigide
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