MATH 422 ABSTRACT ALGEBRA II

Course Syllabus

1. Topics from Group Theory
1. Direct Products of Groups
2. Finitely Generated Abelian Groups
3. Solvable Groups
4. Sylow Theorems
2. Polynomial Rings
3. Division Algorithm in F [x]
4. Irreducible Polynomials
5. Ideal Structure in F [x]
6. Unique Factorization in F [x]
7. Fields
1. Algebraic Elements
2. Finite and Algebraic Extensions
3. Geometric Constructions
4. Splitting Fields
5. Finite Fields

Prerequisite: MATH 421

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