Rings and Fields
Graham Ellis(Author)
Clarendon Press
Book
Paperback/Softback
178 pages
978-0-19-853454-9 (ISBN)
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. Rather than presenting theory in abstract terms, chapters begin by introducing a problem and then go on to develop the necessary algebraic techniques for its solution, using concrete mathematical and non-mathematical examples. Although prior knowledge of group theory is unnecessary to understand the rest of the book, for those interested there is a chapter which states the axiom for a group and proves the group theoretic results needed in Galois theory.
More details
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Oxford University Press
Target group
College/higher education
Illustrations
22 line drawings, bibliography, index
Dimensions
Height: 230 mm
Width: 150 mm
Weight
431 gr
ISBN-13
978-0-19-853454-9 (9780198534549)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Person
Content
Preliminaries; diophantine equations - Euclidean domains; construction of projective planes - splitting fields and finite fields; error codes - primitive elements and subfields; construction of primitive polynomials - cyclotomic polynomials and factorization; ruler and compass constuctions - irreducibility and constructibility; Pappus' theorem and Desargues' theorem in projective planes - Wedderburn's theorem; solution of polynomials by radicals- Galois groups; introduction to groups; cryptography - elliptic curves and factorization.