Math 480, Spring 2014, Assignment 3
From cartan.math.umb.edu
Carefully define the following terms, then give one example and one non-example of each:
- $\mathsf{k}$-algebra.
- Homomorphism of $\mathsf{k}$-algebras.
- Pullback map (associated with a given regular map).
Carefully state the following theorems (you need not prove them):
- Theorem relating regular maps of varieties to $\mathsf{k}$-algebra homomorphisms of their coordinate rings.
- Theorem relating isomorphisms of varieties to isomorphisms of their coordinate rings.
Solve the following problems:
- Section 5.4, problems 1, 6, and 14.