Math 480, Spring 2014, Assignment 3

Carefully define the following terms, then give one example and one non-example of each:

1. $\mathsf{k}$-algebra.
2. Homomorphism of $\mathsf{k}$-algebras.
3. Pullback map (associated with a given regular map).

Carefully state the following theorems (you need not prove them):

1. Theorem relating regular maps of varieties to $\mathsf{k}$-algebra homomorphisms of their coordinate rings.
2. Theorem relating isomorphisms of varieties to isomorphisms of their coordinate rings.

Solve the following problems:

1. Section 5.4, problems 1, 6, and 14.

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