Math 360, Fall 2014, Assignment 11

The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell.

- Saint Augustine

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

1. Ring.
2. Commutative ring.
3. Unity.
4. Unital ring.
5. Unit.
6. Homomorphism, monomorphism, epimorphism, isomorphism (of rings).
7. Unital homomorphism.
8. Division ring.
9. Field.
10. Subring.
11. Subfield.

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

1. Laws of sign.

Solve the following problems:

1. Section 18, problems 1, 7, 9, 11, 12, 14, 15, 16, and 19.

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