Mathematics 894 Problem Set 8

Due date: Friday March 14. 1. Page 529, #1

2. Page 530, #7

3. Page 530, #8

4. Page 530, #13

5. Page 530, #14

6. Consider the diagram of fields

[figure: F G; F; G; K]

Prove that a K-basis of F is a spanning set of F G over G. Conclude from this that [F G : G] ≤ [F : K].