Math 360, Fall 2014, Assignment 12

"Reeling and Writhing, of course, to begin with," the Mock Turtle replied; "And then the different branches of Arithmetic - Ambition, Distraction, Uglification, and Derision."

- Lewis Carroll, Alice's Adventures in Wonderland

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 unital ring).

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

1. Theorem concerning zero-divisors and units of $\mathbb{Z}_n$.
2. Cancellation laws.
3. Theorem relating fields to integral domains.
4. Theorem relating unital subrings of fields to integral domains.

Solve the following problems:

1. Section 19, problems 1, 5, 7, 9, and 14.

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