Pierre Samuel

Algebraic Theory of Numbers (eBook, ePUB)

Translated from the French by Allan J. Silberger

• Format: ePub

Produktbeschreibung

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.

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Produktdetails

• Verlag: Guilford Publications
• Seitenzahl: 112
• Erscheinungstermin: 12. März 2013
• Englisch
• ISBN-13: 9780486318271
• Artikelnr.: 39074361

Inhaltsangabe

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