Algebraic Theory of Numbers

Algebraic Theory of Numbers

3.66 (6 ratings by Goodreads)
By (author)  , Translated by 

Free delivery worldwide

Available. Dispatched from the UK in 2 business days
When will my order arrive?

Description

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.
show more

Product details

  • Paperback | 112 pages
  • 152.4 x 231.14 x 7.62mm | 158.76g
  • New York, United States
  • English
  • black & white illustrations
  • 0486466663
  • 9780486466668
  • 282,681

Table of contents

Translator's IntroductionIntroductionNotations, Definitions, and Prerequisites1. Principal ideal rings2. Elements integral over a ring; elements algebraic over a fieldAppendix: The field of complex numbers is algebraically closed3. Noetherian rings and Dedekind rings4. Ideal classes and the unit theoremAppendix: The calculation of a volume5. The splitting of prime ideals in an extension field6. Galois extensions of number fieldsA supplement, without proofsExercisesBibliographyIndex
show more

Rating details

6 ratings
3.66 out of 5 stars
5 17% (1)
4 33% (2)
3 50% (3)
2 0% (0)
1 0% (0)
Book ratings by Goodreads
Goodreads is the world's largest site for readers with over 50 million reviews. We're featuring millions of their reader ratings on our book pages to help you find your new favourite book. Close X