James Cook's Abstract Algebra II Homepage:
Welcome.

Course Materials for Spring 2026 Abstract Algebra II:

• Abstract Algebra II You Tube Playlist (Lectures from Spring 2026)
• Course Plan for Spring 2026


• Lectures for Math 422 of Spring 2026:
  
  • Lecture 1: On Equations and Symmetries
  • Lecture 2: Group Actions and the Class Equation
  • Lecture 3: Sylow Theorems, Classification of Groups, Isomorphism
  • Lecture 4: Rings, definition and basic examples.
  • Lecture 5: Ring Homomorphism and Quotient Rings
  • Lecture 5: Ring Homomorphism and Quotient Rings
  • Lecture 6: Properties of Ideals, prime and maximal ideals
  • Lecture 7: Domain Expansion!in-class, we discussed characteristic of ring, embedded Z or Zn, and field of fractions for an integral domain.
  • Lecture 8: Chinese Remainder Theoremin-class, we also discussed field of fractions based on Dummit and Foote Section 7.5.
  • Lecture 9: Euclidean Domains, primes, irreducibles and associates.
  • Lecture 10: Principal Ideal Domains.
  • Lecture 11: Application of Algebraic Numbers to Number Theory, Unique Factorization Domains.
  • Lecture 12: Construction of Polynomials
  • Lecture 13: division algorithm, evaluation homomorphism, irreducibility of linear
  • Lecture 14: Irreducible Polynomials
  • Lecture 15: Multiple Roots, Rational Roots and Eisenstein Applied, Chinese Remainder applied
• Missions of 2026:
  
  • Mission 1: group actions and rings.
  • Mission 2: field extensions and Galois theory.

my Abstract Algebra I(2018) notes. These are helpful for the first bit of the course which I covered in Math 421.
That said, I'm trying to write lectures specific to this semester.
If I get sick or something, we'll use these probably.

Course Materials from past terms:

1. You Tube Playlist for Math 422 of the Spring 2019 semester
2. You Tube Playlist for Math 422 of the Spring 2018 semester
3. You Tube Playlist for Math 422 of the Spring 2017 semester

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Last Modified: 2-24-2026