Question: > 
> Prove that the only Boolean ring that is an integral domain is $Z/2Z$.
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I know that the definition of a Boolean ring is $a^2=a$ and that an integral domain is $ab=0$ either $a=0$ or $b=0$. But yet i still can not solve the problem any idea please.

Answer: 
**Hint**:

In a Boolean ring:

$a(a-1)=0$
Let $a \in R$. $a^2 = a$, implies that $a^2 - a =0$, $a(a-1)=0$. either $a = 0$ or $a-1=0$, thus $a=1$. Therefore $R$ is $Z/2Z$.