Math 360, Fall 2013, Assignment 12

Algebra begins with the unknown and ends with the unknowable.

- Anon.

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

1. Zero-divisor.
2. (Integral) domain.
3. Characteristic (of a ring).

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

1. Cancellation laws (for an integral domain).
2. Relationship between fields and integral domains (i.e. which fields must be domains, and which domains must be fields).
3. Little Theorem of Fermat.
4. Euler's Theorem.

Solve the following problems:

1. Section 19, problems 1, 5, 7, 9, and 23.
2. Section 20, problems 5, 9, and 10.

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