Math 360, Fall 2017, Assignment 12

"When I think of Euclid even now, I have to wipe my sweaty brow."

- C. M. Bellman

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

1. Image (of a homomorphism).
2. Kernel (of a homomorphism).

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

1. Characterization of epimorphisms in terms of images.
2. Characterization of monomorphisms in terms of kernels.
3. Theorem concerning the normality of kernels.
4. Theorem describing the fibers of a homomorphism.

Solve the following problems:

1. Section 13, problems 16, 17, 19, 44, 45, and 49.

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