A conversational introduction to algebraic number theory : arithmetic beyond Z / Paul Pollack

Von:

Pollack, Paul, 1980- [aut]

Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Reihen: Student Mathematical Library ; v.84Verlag: Providence : American Mathematical Society, 2017Beschreibung: 1 Online-Ressource (329 p)ISBN:

9781470441258

Schlagwörter:

Andere physische Formen: 1470436531 | 9781470436537 | Erscheint auch als: A conversational introduction to algebraic number theory. Druck-Ausgabe Providence, Rhode Island : American Mathematical Society, 2017. ix, 316 SeitenMSC: MSC: *11-01 | 11R04 | 11R11 | 11R27 | 11R29 | 11Y05RVK: RVK: SK 180Online-Ressourcen:

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Zusammenfassung: Gauss famously referred to mathematics as the "queen of the sciences" and to number theory as the "queen of mathematics". This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field \mathbb{Q}. Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three "fundamental theorems": unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While thZusammenfassung: Chapter 13. Back to basics: Starting over with arbitrary number fieldsChapter 14. Integral bases: From theory to practice, and back; Chapter 15. Ideal theory in general number rings; Chapter 16. Finiteness of the class group and the arithmetic of \Z; Chapter 17. Prime decomposition in general number rings; Chapter 18. Dirichlet's unit theorem, I; Chapter 19. A case study: Units in \Z[√[3]2] and the Diophantine equation ³-2 ³=±1; Chapter 20. Dirichlet's unit theorem, II; Chapter 21. More Minkowski magic, with a cameo appearance by Hermite; Chapter 22. Dedekind's discriminant theoremZusammenfassung: Chapter 13. Back to basics: Starting over with arbitrary number fieldsChapter 14. Integral bases: From theory to practice, and back; Chapter 15. Ideal theory in general number rings; Chapter 16. Finiteness of the class group and the arithmetic of \Z; Chapter 17. Prime decomposition in general number rings; Chapter 18. Dirichlet's unit theorem, I; Chapter 19. A case study: Units in \Z[√[3]2] and the Diophantine equation ³-2 ³=±1; Chapter 20. Dirichlet's unit theorem, II; Chapter 21. More Minkowski magic, with a cameo appearance by Hermite; Chapter 22. Dedekind's discriminant theoremZusammenfassung: Gauss famously referred to mathematics as the "queen of the sciences" and to number theory as the "queen of mathematics". This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field \mathbb{Q}. Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three "fundamental theorems": unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While thPPN: PPN: 1003053149Package identifier: Produktsigel: ZDB-4-NLEBK

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