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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: 978-0-8218-3672-9 (print); 978-1-4704-1292-0 (online)
DOI: https://doi.org/10.1090/surv/065
MathSciNet review: MR1657671
MSC: Primary 01A60; Secondary 01A70, 13-03, 16-00, 16-03

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Table of Contents

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Front/Back Matter

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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