Mathematics 4321 Review Test #3 Spring 2007
I. Define the following terms:
II. Study the following theorems:
3. Theorem: A finite field of order exists for every prime power .
4. Theorem: Let K be an extension of F and . If is a root of f(x) and , then is also a root of f(x).
5. Theorem: Let K=F() be an algebraic extension of F. If with for every , then .
6. Theorem: If K is the splitting field of a polynomial f(x) of degree n in F[x], then Gal(K/F) is isomorphic to a subgroup of .
III. Do all assigned problems from Sections 42-46.