Simple Noetherian Rings

This work specifically surveys simple Noetherian rings.

John Cozzens (Author), CArl Faith (Author)

9780521092999, Cambridge University Press

Paperback / softback, published 8 January 2009

156 pages
21.6 x 14 x 0.9 cm, 0.21 kg

This work specifically surveys simple Noetherian rings. The authors present theorems on the structure of simple right Noetherian rings and, more generally, on simple rings containing a uniform right ideal U. The text is as elementary and self-contained as practicable, and the little background required in homological and categorical algebra is given in a short appendix. Full definitions are given and short, complete, elementary proofs are provided for such key theorems as the Morita theorem, the Correspondence theorem, the Wedderburn–Artin theorem, the Goldie–Lesieur–Croisot theorem, and many others. Complex mathematical machinery has been eliminated wherever possible or its introduction into the text delayed as long as possible. (Even tensor products are not required until Chapter 3.)

1. The correspondence theorem for projective modules
2. Structure of Noetherian simple rings
3. Noetherian simple domains
4. Orders in simple Artin rings
5. V-rings
6. PCI-rings
7. Open problems.

Subject Areas: Algebra [PBF]