Ideal Theory

An introduction to the modern theory of ideas.

D. G. Northcott (Author)

9780521604833, Cambridge University Press

Paperback, published 3 June 2004

120 pages
21.5 x 14 x 0.9 cm, 0.169 kg

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.

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.

Subject Areas: Algebra [PBF]