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Algebra: A Graduate Course
About this Title
I. Martin Isaacs, University of Wisconsin, Madison, WI
Publication: Graduate Studies in Mathematics
Publication Year:
2009; Volume 100
ISBNs: 978-0-8218-4799-2 (print); 978-1-4704-1164-0 (online)
DOI: https://doi.org/10.1090/gsm/100
MathSciNet review: MR2472787
MSC: Primary 00-01; Secondary 12-01, 13-01, 16-01, 20-01
Table of Contents
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Front/Back Matter
Part One. Noncommutative algebra
- Chapter 1. Definitions and examples of groups
- Chapter 2. Subgroups and cosets
- Chapter 3. Homomorphisms
- Chapter 4. Group actions
- Chapter 5. The Sylow theorems and $p$-groups
- Chapter 6. Permutation groups
- Chapter 7. New groups from old
- Chapter 8. Solvable and nilpotent groups
- Chapter 9. Transfer
- Chapter 10. Operator groups and unique decompositions
- Chapter 11. Module theory without rings
- Chapter 12. Rings, ideals, and modules
- Chapter 13. Simple modules and primitive rings
- Chapter 14. Artinian rings and projective modules
- Chapter 15. An introduction to character theory
Part Two. Commutative algebra
- Chapter 16. Polynomial rings, PIDs, and UFDs
- Chapter 17. Field extensions
- Chapter 18. Galois theory
- Chapter 19. Separability and inseparability
- Chapter 20. Cyclotomy and geometric constructions
- Chapter 21. Finite fields
- Chapter 22. Roots, radicals, and real numbers
- Chapter 23. Norms, traces, and discriminants
- Chapter 24. Transcendental extensions
- Chapter 25. the Artin-Schreier theorem
- Chapter 26. Ideal theory
- Chapter 27. Noetherian rings
- Chapter 28. Integrality
- Chapter 29. Dedekind domains
- Chapter 30. Algebraic sets and the Nullstellensatz