I've proved that a Boolean ring is a Boolean algebra but I am having trouble with the converse. The operation for + is defined as the symmetric difference for elements $a$ and $b$ from the Boolean algebra and multiplication is standard juxtaposition for $\lor$, $\land$ respectively. I know I must show that under "addition" the Boolean algebra is an Abelian group and then show associativity for multiplication and then the distributive laws. I am stuck with how to show closure of "addition", is it even necessary? I just need a few hints to get on with the proof. Thanks.