Algebra
Group Theory
Ring Theory
- Irreducible, Prime and Associate
- Factorization in Noetherian Domains
- Hilbert Basis Theorem
- Greatest Common Divisors in UFDs
- Gauss’s Lemma
Galois Theory
- Algebraic Elements
- Field Extensions
- Algebraic Closure
- Finite Fields
- Field Automorphisms
- Splitting Fields
- Isomorphism Extension Theorem
- Normal Extensions
- Separable Polynomials
- Separable Extensions and Perfect Fields
- Galois Extensions
- Galois Correspondence Theorem
- Galois Group of Finite Fields
- Cyclotomic Polynomials
- Cyclotomic Extensions
- Kummer’s Theory
- Solvability by Radicals