Math 361, Spring 2016, Assignment 6

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

1. Field extension.
2. Extension field.
3. Base field (or ground field).
4. Subextension (of a field extension).
5. Subextension generated by a subset.
6. Simple extension.
7. Finitely generated extension.
8. Algebraic element (of an extension field).
9. Transcendental element (of an extension field).
10. Monic polynomial.
11. Minimal polynomial (of an algebraic element).

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

1. Classification of simple extensions.

Solve the following problems:

1. Section 29, problems 1, 3, 5, 7, 11, 12, 13, and 14.

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