Thread: Integral Domain

I am having troubles with the following problem:

Show that there is an integral domain with exactly 4 elements.

Any suggestion?

Originally Posted by ynn6871

I am having troubles with the following problem:

Show that there is an integral domain with exactly 4 elements.

Any suggestion?

Let - the polynomials with coefficients in .
Let . This polynomial is irreducible over .
Therefore, all elements in are invertible.
Consequently, is an integral domain with .