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Generative complexity in algebra
About this Title
Joel Berman and PawełM. Idziak
Publication: Memoirs of the American Mathematical Society
Publication Year:
2005; Volume 175, Number 828
ISBNs: 978-0-8218-3707-8 (print); 978-1-4704-0429-1 (online)
DOI: https://doi.org/10.1090/memo/0828
MathSciNet review: 2130585
MSC: Primary 08A05; Secondary 03C13, 03C45, 05A16, 08B20
Table of Contents
Chapters
- 1. Introduction
- 2. Background material
- Part 1. Introducing generative complexity
- 3. Definitions and examples
- 4. Semilattices and lattices
- 5. Varieties with a large number of models
- 6. Upper bounds
- 7. Categorical invariants
- Part 2. Varieties with few models
- 8. Types 4 or 5 need not apply
- 9. Semisimple may apply
- 10. Permutable may also apply
- 11. Forcing modular behavior
- 12. Restricting solvable behavior
- 13. Varieties with very few models
- 14. Restricting nilpotent behavior
- 15. Decomposing finite algebras
- 16. Restricting affine behavior
- 17. A characterization theorem
- Part 3. Conclusions
- 18. Application to groups and rings
- 19. Open problems
- 20. Tables