## Text

Artin, M. Algebra (2nd Edition). Addison Wesley, 2010. ISBN: 9780132413770.

The exercises listed below point to the text and are a suggestion from the professor to the students in every given lecture. These exercises were not turned in and were not corrected.

Group Representations
1 Group representations Chapter 10, sections 1, and 4 Chapter 10, 1.1, and 1.2
2 Unitary representations Chapter 10, sections 2, and 3 Chapter 10, 2.1, 2.2, and 3.4
3 Characters Chapter 10, section 4 Chapter 10, 4.1, 4.3a, b, and 4.8
4 One-dimensional characters Chapter 10, section 5 Chapter 10, 5.1, and 5.3
5 The regular representation Chapter 10, section 6 Chapter 10, 6.1, and 6.10
6 Characters (cont.) Chapter 10, sections 7, and 8 Chapter 10, 7.1, 7.2, and 7.6
Rings: Basic Definitions
7 Rings, ring homomorphisms Chapter 11, sections 1, 2, and 3 Chapter 11, 1.1, 1.5, 1.8, and 1.9
8 Ideals, quotient rings, correspondence theorem Chapter 11, sections 4, and 5 Chapter 11, 3.12, 3.13, 4.1, and 4.2
9 Maximal ideals, prime ideals, fractions Chapter 11, sections 8, and 9 Chapter 11, 6.1, 7.1, and 8.3
Rings: Factoring
10 Gauss’ Lemma Chapter 12, section 3 Chapter 12, 2.3, 2.7, and 3.2
11 Unique factorization Chapter 12, sections 1, and 2 Chapter 12, 1.1, 1.5, 2.1, and 2.2
12 Factoring integer polynomials Chapter 12, section 4 Chapter 12, 4.1a, 4.6, 4.7, and 4.11
13 Gauss primes Chapter 12, section 5 Chapter 12, 5.1, 5.2a, and 5.3
14 Quadratic integers Chapter 13, section 1 Chapter 13, 1.1, 1.2, and 1.3
15 Ideal factorization Chapter 13, sections 2, and 3 Chapter 13, 2.1, 3.1, 3.2, and 3.3
16 Prime ideals Chapter 13, sections 5, and 6 Chapter 13, 5.3, 6.1, and 6.2
17 Ideal classes Chapter 11, sections 9, and 10 Chapter 13, 7.1, 7.2, and 8.2
Linear Algebra over a Ring
18 Integer matrices Chapter 14, sections 1, and 2 Chapter 14, 1.1, 2.1, and 2.4
19 Free modules Chapter 14, sections 3, and 4 Chapter 14, 3.2, 4.1a, and 4.3
20 Presenting modules Chapter 12, section 5 Chapter 14, 5.1, and 5.2
21 Hilbert basis theorem Chapter 14, section 6 Chapter 11, 6.1, 6.2, and M.1
22 Structure of abelian groups Chapter 14, section 7 Chapter 14, 7.1, 7.2, and 7.5
23 Linear operators Chapter 14, section 8 Chapter 14, 8.1, 8.3, and 8.4
Fields: Field Extensions
24 Algebraic elements, degree Chapter 15, sections 1, and 2 Chapter 15, 1.1, 1.3, and 2.1
25 Ruler and compass Chapter 13, section 5 Chapter 15, 5.1, 5.2, and 5.4
26 Adjoining elements Chapter 11, section 5, chapter 15, section 6 Chapter 11, 5.2, and 5.3, chapter 15, 6.1, and 6.3
27 Finite fields Chapter 15, section 7 Chapter 15, 7.1, 7.2, and 7.13
28 Primitive elements Chapter 15, section 8 Chapter 15, 8.1, and 8.2
Fields: Galois Theory
29 Symmetric functions, discriminant Chapter 16, sections 1, and 2 Chapter 16, 1.1a, b, e, 2.1, and 2.2
30 Splitting fields, the Galois group Chapter 16, sections 3, and 4 Chapter 16, 3.2, and 4.1
31 Fixed fields, Galois extensions Chapter 16, sections 5, and 6 Chapter 16, 5.1b, c, 6.1, and 6.2
32 The main theorem Chapter 16, section 7 Chapter 16, 7.1, 7.3, 7.6, and 7.7
33 Cubic and quartic equations Chapter 16, sections 8, and 9 Chapter 16, 8.2a, b, c, 9.1, 9.3, and 9.6
34 Quartic equations (cont.)

Chapter 16, section 9

Handout on The Seventeengon (PDF)

Chapter 16, 9.12a, b, and 9.16
35 Roots of unity, Kummer extensions Chapter 16, sections 10, and 11 Chapter 16, 10.1, 10.3, and 11.1
36 Quintic equations Chapter 16, section 12 Chapter 16, 12.1, 12.2, and 12.7

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assignment Problem Sets