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

III. Rings.

• Section III.1. Rings and Homomorphisms. Section III.1 notes
• Supplement. Proofs of Theorems in Section III.1. Beamer file of Section III.1 proofs
• Supplement. Printout of the Proofs of Theorems in Section III.1. Print file of Section III.1 proofs
• Section III.2. Ideals. Section III.2 notes
• Supplement. Proofs of Theorems in Section III.2. Beamer file of Section III.2 proofs
• Supplement. Printout of the Proofs of Theorems in Section III.2. Print file of Section III.2 proofs
• Section III.3. Factorization in Commutative Rings. Section III.3 notes
• Supplement. Proofs of Theorems in Section III.3. Beamer file of Section III.3 proofs
• Supplement. Printout of the Proofs of Theorems in Section III.3. Print file of Section III.3 proofs
• Section III.3 Supplement. Gaussian Integers. Section III.3 Gaussian Integers notes
• Supplement. Proofs of Theorems in Section III.3. Beamer file of Section III.3 Gaussian Integers proofs
• Supplement. Printout of the Proofs of Theorems in Section III.3. Print file of Section III.3 Gaussian Integers proofs
• Section III.4. Rings of Quotients and Localization. Section III.4 notes (This section includes the price paid for trying to "divide by 0" in a ring of quotients; see Note III.4.B.)
• Supplement. Proofs of Theorems in Section III.4. Beamer file of Section III.4 proofs
• Supplement. Printout of the Proofs of Theorems in Section III.4. Print file of Section III.4 proofs
• Section III.5. Rings of Polynomials and Formal Power Series. Section III.5 notes
• Supplement. Proofs of Theorems in Section III.5. Beamer file of Section III.5 proofs
• Supplement. Printout of the Proofs of Theorems in Section III.5. Print file of Section III.5 proofs
• Section III.6. Factorization in Polynomial Rings. Section III.6 notes
• Supplement. Proofs of Theorems in Section III.6. Beamer file of Section III.6 proofs
• Supplement. Printout of the Proofs of Theorems in Section III.6. Print file of Section III.6 proofs
• Supplement. Quaternions - An Algebraic View. Quaternions - Algebraic View notes
  • Supplement. Proofs of Theorems in Quaternions - An Algebraic View. Beamer file of Quaternions - Algebraic View proofs
  • Supplement. Printout of the Proofs of Theorems in Quaternions - An Algebraic View. Print file of Quaternions - Algebraic View proofs.
• Supplement. Quaternions - An Algebraic View (in PowerPoint with some history): Quaternions - Algebraic View (with history) in PowerPoint.
• Supplement. Quaternions - The Degree of a Polynomial versus the Number of Zeros (partial). Quaternions - Degree of Polynomial and Number of Zeros notes
• Study Guide III

IV. Modules. Chapter IV Introduction notes

• Section IV.1. Modules, Homomorphisms, and Exact Sequences. Section IV.1 notes (Includes a statement of the Snake Lemma; see Note IV.1.J.)
• Supplement. Proofs of Theorems in Section IV.1. Beamer file of Section IV.1 proofs
• Supplement. Printout of the Proofs of Theorems in Section IV.1. Print file of Section IV.1 proofs
• Supplement. A Proof of the Snake Lemma. Snake Lemma notes
• Section IV.2. Free Modules and Vector Spaces. Section IV.2 notes (This section includes a proof that there is no field strictly between ℝ and ℂ; see Note IV.2.K.)
• Supplement. Proofs of Theorems in Section IV.2. Beamer file of Section IV.2 proofs
• Supplement. Printout of the Proofs of Theorems in Section IV.2. Print file of Section IV.2 proofs
• Section IV.3. Projective and Injective Modules. Section IV.3 notes
• Supplement. Proofs of Theorems in Section IV.3 (partial). Beamer file of Section IV.3 proofs
• Supplement. Printout of the Proofs of Theorems in Section IV.3. Print file of Section IV.3 proofs
• Section IV.4. Hom and Duality.
• Section IV.5. Tensor Products.
• Section IV.6. Modules over a Principal Ideal Domain (partial). Section IV.6 notes
• Section IV.7. Algebras. Section IV.7 notes
• Supplement. Proofs of Theorems in Section IV.7 (partial). Beamer file of Section IV.7 proofs
• Supplement. Printout of the Proofs of Theorems in Section IV.7 (partial). Print file of Section IV.7 proofs
• Study Guide IV.

VIII. Commutative Rings and Modules.

• Section VIII.1. Chain Conditions. Section VII.1 notes
• Supplement. Proofs of Theorems in Section VIII.1. Beamer file of Section VIII.1 proofs
• Supplement. Printout of the Proofs of Theorems in Section VIII.1. Print file of Section VIII.1 proofs
• Section VIII.2. Prime and Primary Ideals.
• Section VIII.3. Primary Decompositions.
• Section VIII.4. Noetherian Rings and Modules.
• Section VIII.5. Ring Extensions.
• Section VIII.6. Dedekind Domains.
• Section VIII.7. The Hilbert Nullstellensatz.
• Study Guide VIII.

IX. The Structure of Rings.

• Section IX.1. Simple and Primitive Rings. Section IX.1 notes
• Supplement. Proofs of Theorems in Section IX.1. Beamer file of Section IX.1 proofs
• Supplement. Printout of the Proofs of Theorems in Section IX.1. Print file of Section IX.1 proofs
• Section IX.2. The Jacobson Radical. Section IX.2 notes
• Supplement. Proofs of Theorems in Section IX.2. Beamer file of Section IX.2 proofs
• Supplement. Printout of the Proofs of Theorems in Section IX.2. Print file of Section IX.2 proofs
• Section IX.3. Semisimple Rings. Section IX.3 notes
• Supplement. Proofs of Theorems in Section IX.3 (partial). Beamer file of Section IX.3 proofs
• Supplement. Printout of the Proofs of Theorems in Section IX.3 (partial). Print file of Section IX.3 proofs
• Section IX.4. The Prime Radical; Prime and Semiprime Rings.
• Section IX.5. Algebras.
• Section IX.6. Division Algebras.
• Supplement. The Cayley-Dickson Construction and Nonassociative Algebras. Cayley-Dickson Construction notes (This is a section notes used in Introduction to Modern Algebra 2 [MATH 4137/5137] contains the development of the quaternions, octonions, sedenions, etc.)
• Supplement. Proofs of Theorems in the Cayley-Dickson Supplement. Beamer file of Cayley-Dickson Supplement proofs
• Supplement. Printout of the Proofs of Theorems in the Cayley-Dickson Supplement. Print file of Cayley-Dickson Supplement proofs
• Study Guide IX.

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