Math 361, Spring 2015, Assignment 8

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

1. Finite extension. (Warning: these may in fact be infinite objects.)
2. Degree (of a finite extension).
3. Degree (of an algebraic element of a field extension).

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

1. Theorem relating finite extensions to algebraic extensions (Theorem 31.3).
2. Dimension formula (Theorem 31.4).
3. Lagrange-like theorem for degrees of elements of finite extensions (this is not stated in the book, but is similar to Corollary 31.7).

Solve the following problems:

1. Section 31, problems 3, 5, 11, 23, 24, 25, and 29.

--------------------End of assignment--------------------