# Rings and Things and a Fine Array of Twentieth Century Associative Algebra, Second Edition

### About this Title

**Carl Faith**, *Professor Emeritus, Rutgers University, New Brunswick, NJ*

Publication: Mathematical Surveys and Monographs

Publication Year
1999: Volume 65

ISBNs: 978-0-8218-0993-8 (print); 978-1-4704-1292-0 (online)

DOI: http://dx.doi.org/10.1090/surv/065

MathSciNet review: MR1657671

MSC (1991): Primary 01A60; Secondary 01A70, 13-03, 16-00, 16-03

### Table of Contents

**Front/Back Matter**

**Chapters**

- 1. Direct product and sums of rings and modules and the structure of fields
- 2. Introduction to ring theory: Schur's Lemma and semisimple rings, prime and primitive rings, Noetherian and Artinian modules, nil, prime and Jacobson radicals
- 3. Direct decompositions of projective and injective modules
- 4. Direct product decompositions of von Neumann regular rings and self-injective rings
- 5. Direct sums of cyclic modules
- 6. When injectives are flat: Coherent FP-injective rings
- 7. Direct decompositions and dual generalizations of Noetherian rings
- 8. Completely decomposable modules and the Krull-Schmidt-Azumaya theorem
- 9. Polynomial rings over Vamosian and Kerr rings, valuation rings and Prüfer rings
- 10. Isomorphic polynomial rings and matrix rings
- 11. Group rings and Maschke's theorem revisited
- 12. Maximal quotient rings
- 13. Morita duality and dual rings
- 14. Krull and global dimensions
- 15. Polynomial identities and PI-rings
- 16. Unions of primes, prime avoidance, associated prime ideals, ACC on irreducible ideals, and Annihilator ideals in commutative rings
- 17. Dedekind's theorem on the independence of automorphisms revisited
- 18. Snapshots of some mathematical friends and places