Homework solutions for LSU MATH 7220, Commutative Algebra.
The course description is "We will cover the basics of Commutative Algebra and give an introduction to the elements of Algebraic Geometry of affine and projective varieties. This will be a preparation for learning the theory of Schemes. Topics include:
- Affine and projective varieties
- Prime and Maximal Ideals
- Localization
- Integral extensions
- Primary decomposition
- Dimension; Hilbert-Samuel polynomial
- Homological methods; Free resolutions
- Kähler differentials
- Flat, smooth and étale morphisms"
Problems mostly come from the instructor, sometimes from textbooks such as the famous ones Atiyah-MacDonald and Eisenbud.
There may be errors or typos! You have been warned!