Characteristic of an integral domain

• Sep 18th 2009, 01:53 PM
akolman
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.
• Sep 18th 2009, 01:55 PM
NonCommAlg
Quote:

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.
• Sep 18th 2009, 02:15 PM
akolman