Math 361, Spring 2014, Assignment 13

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

1. Group presentation.
2. Generators (of a given presentation).
3. Relators (of a presentation).
4. Finitely presented group.
5. Isomorphic presentations.
6. Irreducible element (of a domain $D$).
7. Prime element (of a domain $D$).

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

1. Theorem relating unique factorization to divisor chains and primeness.
2. Theorem relating unique factorization in $D$ to unique factorization in $D[x]$.
3. Theorem concerning factorization in principal ideal domains.

Solve the following problems:

1. Section 40, problems 1, 3, and 5.
2. Section 45, problems 1, 3, 5, 7, and 9.

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