Math 361, Spring 2014, Assignment 4

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

1. Algebraic element (of an extension field).
2. Minimal polynomial (of an algebraic element).
3. Conjugate (of an algebraic element).
4. Subextension generated by a subset.
5. Finitely generated extension.
6. Simple extension.

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

1. Classification of simple extensions.

Solve the following problems:

1. Section 29, problems 1, 5, 7, 11, and 13.

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