# Math Help - Characteristic of an integral domain

1. ## Characteristic of an integral domain

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

Let $D$ be an integral domain, with 4 elements $D=\{0,e,a,b\}$, where $e$ is the unity. Prove that $D$ has characteristic 2.

Thanks again.

2. Originally Posted by akolman
I suppose this should be an easy question. However, I am stuck with this:

Let $D$ be an integral domain, with 4 elements $D=\{0,e,a,b\}$, where $e$ is the unity. Prove that $D$ 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.

3. Thanks again for your help.