Rings and Fields

Name: Rings and Fields
Availability: OutOfStock
ISBN: 9780198534549

ISBN-10: 019853454X

ISBN-13: 9780198534549

Edition: 1992

Authors: Graham Ellis

List price: $15.95

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Description:

This book aims to provide an accessible introduction to rings and fields that will give the reader an appreciation of the power of algebraic techniques to handle diverse and difficult problems. A review of the prerequisite mathematics is given at the start of the book.

Book details

List price: $15.95
Copyright year: 1992
Publisher: Oxford University Press, Incorporated
Binding: Paperback
Pages: 178
Size: 5.91" wide x 9.06" long
Weight: 0.946
Language: English

Preliminaries	p. 1
Definition of rings and fields
Vector spaces
Bases
Equivalence relations
Axiom of choice
Diophantine equations: Euclidean domains	p. 13
Euclidean domain of Gaussian integers
Euclidean domains as unique factorization domains
Construction of projective planes: splitting fields and finite fields	p. 25
Existence and uniqueness of splitting fields and of finite fields of prime power order
Error codes: primitive elements and subfields	p. 49
Existence of primitive elements in finite fields
Subfields of finite fields
Computation of minimum polynomials
Construction of primitive polynomials: cyclotomic polynomials and factorization	p. 65
Basic properties of cyclotomic polynomials
Berlekamp's factorization algorithm
Ruler and compass constructions: irreducibility and constructibility	p. 83
Product formula for the degree of composite extensions
Irreducibility criteria for polynomials over the rationals
The field of constructible real numbers
Pappus' theorem and Desargues' theorem in projective planes: Wedderburn's theorem	p. 93
Proof of Wedderburn's theorem
Solution of polynomials by radicals: Galois groups	p. 109
Basic definitions and results in Galois groups
Discriminants
Introduction to groups	p. 135
Group axioms
Subgroup lattice
Class equation
Cauchy's theorem
Transitive permutation groups
Soluble groups
Crytography: elliptic curves and factorization	p. 151
Euler's function
Discrete logarithms
Elliptic curves
Pollard's method of factorizing integers
Elliptic curve factorization of integers
Further reading	p. 166
Index	p. 167
Table of Contents provided by Blackwell. All Rights Reserved.