HW
上课
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- 1.1 Review of Groups
- 1.2 Free Abelian Group
- 1.3 Finitely Generated Abelian Group
- 1.4 Group Action on a Set
- 1.5 Sylow Theorem
- 1.6 Nilpotent and Solvable Group
- 1.7 Normal and Subnormal Series
- 2.1 Review of Rings
- 2.2 Modules
- 2.3 Noetherian Rings and Modules
- 2.4 PID and Euclidean domain
- 2.5 Module over PID
- 3.1 Field Extension
- 3.2 Splitting Fields, Normal Extension and Separable Extensions
- 3.3 Galois Extension
- 3.4 Group Characters
- 3.5 Proof of Fundamental Theorem of Galois Theory
- 3.6 Finite Field
- 3.7 Elementary Symmetric Polynomial
- 3.8 Galois Group of a Polynomial
- 3.9 Cyclic and Cyclotomic (分圆) Extension
- 3.10 Radical Extensions