# Integral domains, Principle Ideal domains, Fields

For each of the following rings answer the following questions:

1. Is it an integral domain?

2. Is it a principal ideal domain (PID)?

3. Is it a field?

Give reasons (i.e. short proofs, if needed) for your answer.

1. Z/13Z;

2. Z/20Z;

3. ZÃ?Z with componentwise addition and multiplication;

4. Q[X]/(f) with f=X^2+X+1;

5. C[X]/(f) with f=X^2+X+1;

6. Z[X];

7. R[X] with R=Z/4Z;

8. R[X]/I with R=Z/2Z and I=(X^2+X+1).

https://brainmass.com/math/integrals/integral-domains-principle-ideal-domains-fields-395218

#### Solution Summary

This solution evaluates integral domains, principle ideal domains, and fields.

$2.19