This section contains solutions to selected problems from Artin's
*Algebra*, 2nd ed. I have skipped most of the chapters, focusing on
finite groups, rings, and fields. I have also skipped certain
sections that I didn't find interesting or useful, as well as certain
problems (especially those that seemed too tedious).

I use the convention that 0 is a natural number, Artin be damned.

I will probably not be solving any more problems in this book, but you may feel free to email me with errata, or to contribute better solutions that can be understood using material covered by the appropriate point in the text.

- Chapter 2: Groups
- Section 2.1: Laws of Composition
- Section 2.2: Groups and Subgroups
- Section 2.3: Subgroups of the Additive Group of Integers
- Section 2.4: Cyclic Groups
- Section 2.5: Homomorphisms
- Section 2.6: Isomorphisms
- Section 2.8: Cosets
- Section 2.11: Product Groups
- Section 2.12: Quotient Groups
- Miscellaneous problems for Chapter 2

- Chapter 6: Symmetry
- Chapter 7: More Group Theory
- Section 7.2: The Class Equation
- Section 7.3: \(p\)-Groups
- Section 7.4: The Class Equation of the Icosahedral Group
- Section 7.5: Conjugation in the Symmetric Group
- Section 7.6: Normalizers
- Section 7.7: The Sylow Theorems
- Section 7.8: The Groups of Order 12
- Section 7.10: Generators and Relations
- Miscellaneous problems for chapter 7

- Chapter 11: Rings
- Section 11.1: Definition of a Ring
- Section 11.2: Polynomial Rings
- Section 11.3: Homomorphisms and Ideals
- Section 11.4: Quotient Rings
- Section 11.5: Adjoining Elements
- Section 11.6: Product Rings
- Section 11.7: Fractions
- Section 11.8: Maximal Ideals
- Section 11.9: Algebraic Geometry
- Miscellaneous problems for chapter 11

- Chapter 15: Fields
- Section 15.1: Examples of Fields
- Section 15.2: Algebraic and Transcendental Elements
- Section 15.3: The Degree of a Field Extension
- Section 15.4: Finding the Irreducible Polynomial
- Section 15.5: Constructions with Ruler and Compass
- Section 15.6: Adjoining Roots
- Section 15.7: Finite Fields
- Section 15.8: Primitive Elements
- Section 15.10: The Fundamental Theorem of Algebra
- Miscellaneous problems for chapter 15

- Chapter 16: Galois Theory
- Section 16.1: Symmetric Functions
- Section 16.2: The Discriminant
- Section 16.3: Splitting Fields
- Section 16.4: Isomorphisms of Field Extensions
- Section 16.5: Fixed Fields
- Section 16.6: Galois Extensions
- Section 16.7: The Main Theorem
- Section 16.8: Cubic Equations
- Section 16.9: Quartic Equations
- Section 16.10: Roots of Unity
- Section 16.11: Kummer Extensions
- Section 16.12: Quintic Equations
- Miscellaneous problems for chapter 16