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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

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Table of Contents

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Front/Back Matter

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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