Rings and Fields

ISBN-13: 9780198534556 / Angielski / Twarda / 1993 / 184 str.

Graham Ellis

Opis

This accessible introduction to the mathematics of rings and fields shows how algebraic techniques can be used to solve many difficult problems. The book is carefully organized. Prerequisite mathematical skills are introduced at the beginning, and each chapter opens with an introduction to a problem followed by the development of the algebraic techniques necessary for its solution, using concrete mathematical and non-mathematical examples. Although prior knowledge of group theory is not required, a chapter is included which states the axiom for a group and proves the group theoretic results needed in Galois theory. The work is intended for advanced students and researchers in mathematics, computer science, and electronic engineering.

Recenzje

'Clearly, this book is not meant to compete with comprehensive and systematic expositions of algebra. However, the mixture of applications and theory provides an interesting supplement.' Mathematics Abstracts, 773/93

Spis treści

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; Rule and compass constructions: 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; Further reading; Index.