Thread: Characteristic of an integral domain

I suppose this should be an easy question. However, I am stuck with this:

Let be an integral domain, with 4 elements , where is the unity. Prove that has characteristic 2.

Thanks again.

Originally Posted by akolman

I suppose this should be an easy question. However, I am stuck with this:

Let be an integral domain, with 4 elements , where is the unity. Prove that has characteristic 2.

Thanks again.

characteristic of a finite integral domain is always a prime number. it also has to divide the order of ring, which is 4. so it has to be 2.

Thanks again for your help.