Lessons on Rings, Modules and Multiplicities
Cambridge University Press, 3/9/2009
EAN 9780521098076, ISBN10: 0521098076
Paperback, 460 pages, 22.9 x 15.2 x 2.6 cm
Language: English
This volume provides a clear and self-contained introduction to important results in the theory of rings and modules. Assuming only the mathematical background provided by a normal undergraduate curriculum, the theory is derived by comparatively direct and simple methods. It will be useful to both undergraduates and research students specialising in algebra. In his usual lucid style the author introduces the reader to advanced topics in a manner which makes them both interesting and easy to assimilate. As the text gives very full explanations, a number of well-ordered exercises are included at the end of each chapter. These lead on to further significant results and give the reader an opportunity to devise his own arguments and to test his understanding of the subject.
Preface
Some notes for the reader
1. Introduction to some basic ideas
2. Prime ideals and primary submodules
3. Rings and modules of fractions
4. Noetherian rings and modules
5. The theory of grade
6. Hilbert rings and the Zeros Theorem
7. Multiplicity theory
8. The Koszul complex
9. Filtered rings and modules
Index.