A0 5. Irreducibility and factorization in integral domains

Section 1: Chain conditions and existence of factorizations ✅

• Notes
• Exercise 1.1
• Exercise 1.2
• Exercise 1.3
• Exercise 1.4
• Exercise 1.5
• Exercise 1.6
• Exercise 1.7
• Exercise 1.8
• Exercise 1.9
• Exercise 1.10
• Exercise 1.11
• Exercise 1.12
• Exercise 1.13
• Exercise 1.14
• Exercise 1.15
• Exercise 1.16
• Exercise 1.17

Section 2: UFDs, PIDs, Euclidean domains ✅

• Exercise 2.1
• Exercise 2.2
• Exercise 2.3 TODO
• Exercise 2.4
• Exercise 2.5
• Exercise 2.6
• Exercise 2.7
• Exercise 2.8
• Exercise 2.9
• Exercise 2.10
• Exercise 2.11
• Exercise 2.12
• Exercise 2.13
• Exercise 2.14
• Exercise 2.15
• Exercise 2.16
• Exercise 2.17
• Exercise 2.18
• Exercise 2.19
• Exercise 2.20
• Exercise 2.21
• Exercise 2.22
• Exercise 2.23
• Exercise 2.24
• Exercise 2.25

Section 3: Intermezzo: Zorn’s lemma

• Exercise 3.1
• Exercise 3.2
• Exercise 3.3
• Exercise 3.4
• Exercise 3.5
• Exercise 3.6
• Exercise 3.7
• Exercise 3.8
• Exercise 3.9
• Exercise 3.10 TODO
• Exercise 3.11
• Exercise 3.12
• Exercise 3.13
• Exercise 3.14
• Exercise 3.15

Section 4: Unique factorization in polynomial rings

Section 5: Irreducibility of polynomials

Section 6: Further remarks and examples