Ideal Theory

by D. G. Northcott

Overview

Ideal theory is important not only for the intrinsic interest and purity of its logical structure but because it is a necessary tool in many branches of mathematics. In this introduction to the modern theory of ideals, Professor Northcott assumes a sound background of mathematical theory but no previous knowledge of modern algebra. After a discussion of elementary ring theory, he deals with the properties of Noetherian rings and the algebraic and analytical theories of local rings. In order to give some idea of deeper applications of this theory the author has woven into the connected algebraic theory those results which play outstanding roles in the geometric applications.

Product Details

ISBN-13:	9780521604833
Publisher:	Cambridge University Press
Publication date:	06/03/2004
Series:	Cambridge Tracts in Mathematics , #42
Edition description:	New Edition
Pages:	120
Product dimensions:	5.51(w) x 8.46(h) x 0.35(d)

Table of Contents

Author's preface; Preliminaries; 1. The primary decomposition; 2. Residue rings and rings of quotients; 3. Some fundamental properties of noetherian rings; 4. The algebraic theory of local rings; 5. The analytic theory of local rings; Notes; References; Index of definitions.