Math 361, Spring 2013, Assignment 3

No doubt many people feel that the inclusion of mathematics among the arts is unwarranted. The strongest objection is that mathematics has no emotional import. Of course this argument discounts the feelings of dislike and revulsion that mathematics induces....

- Morris Kline, Mathematics in Western Culture

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

1. Ring homomorphism.
2. Kernel (of a ring homomorphism).
3. Image (of a ring homomorphism).
4. Ideal.
5. Factor ring.

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

1. Fundamental theorem on homomorphisms (either as we stated it in class, or as stated in Theorem 26.17 in the book; don't get confused by mixing the two statements).

Solve the following problems:

1. Section 26, problems 3, 9, 11, 15, and 17.

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