Copies of the classnotes are on the internet in PDF format as given below.

Introduction and Properties of Quaternionic Polynomials (not from Lam)

• The Quaternions: An Algebraic Approach. PowerPoint (presented to the ETSU Abstract Algebra Club, Spring 2017).
• The Quaternions: An Algebraic and Analytic Exploration. PDF (presented at Auburn University, August 7, 2018).

Preface.

• Introduction. PDF.

Chapter 1. Wedderburn-Artin Theory.

• Section 1.1. Basic Terminology and Examples (partial). PDF.
• Supplement. Proofs of Theorems in Section 1.1. PDF (prepared in Beamer).
• Supplement. Printout of the Proofs of Theorems in Section 1.1. PDF.
• Section 1.2. Semisimplicity.
• Section 1.3. Structure of Semisimple Rings.
• Study Guide 1.

Chapter 2. Jacobson Radical Theory.

• Section 2.4. The Jacobson Radical.
• Section 2.5. Jacobson Radical Under Change of Rings.
• Section 2.6. Group Rings and the J-Semisimplicity Problem.
• Study Guide 2.

Chapter 3. Introduction to Representation Theory.

• Section 3.7. Modules over Finite-Dimenisional Algebras.
• Section 3.8. Representations of Groups.
• Section 3.9. Linear Groups.
• Study Guide 3.

Chapter 4. Prime and Primitive Rings.

• Section 4.10. The Prime Radical; Prime and Semiprime Rings.
• Section 4.11. Structure of Primitive Rings; the Density Theorem.
• Section 4.12. Subdirect Products and Commutativity Theorem.
• Study Guide 4.

Chapter 5. Introduction to Division Rings.

• Section 5.13. Division Rings.
• Section 5.14. Some Classical Constructions.
• Section 5.15. Tensor Products and Maximal Subfields.
• Section 5.16. Polynomials over Division Rings.
• Study Guide 5.

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