Algebraic Theory Of Numbers. Questo articolo non è disponibile.
Samuel, Pierre; Silberger, Alan J. (TRN)
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Lingua: inglese
Editore: Dover Publications, 2008
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Codice articolo 5546609-5
- Titolo
- Algebraic Theory Of Numbers
- Autore
- Samuel, Pierre; Silberger, Alan J. (TRN)
- Editore
- Dover Publications
- Anno di pubblicazione
- 2008
- Condizione
- good
- Rilegatura
- Brossura
- Lingua
- inglese
- ISBN 10
- 0486466663
- ISBN 13
- 9780486466668
Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics — algebraic geometry, in particular.
This book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Galois theory, Noetherian rings and modules, and rings of fractions. It covers the basics, starting with the divisibility theory in principal ideal domains and ending with the unit theorem, finiteness of the class number, and the more elementary theorems of Hilbert ramification theory. Numerous examples, applications, and exercises appear throughout the text.
This book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Galois theory, Noetherian rings and modules, and rings of fractions. It covers the basics, starting with the divisibility theory in principal ideal domains and ending with the unit theorem, finiteness of the class number, and the more elementary theorems of Hilbert ramification theory. Numerous examples, applications, and exercises appear throughout the text.
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Contenuti
Translator's Introduction Introduction Notations, Definitions, and Prerequisites 1. Principal ideal rings 2. Elements integral over a ring; elements algebraic over a field Appendix: The field of complex numbers is algebraically closed 3. Noetherian rings and Dedekind rings 4. Ideal classes and the unit theorem Appendix: The calculation of a volume 5. The splitting of prime ideals in an extension field 6. Galois extensions of number fields A supplement, without proofs Exercises Bibliography Index
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