Boolean ring

Remarks

In a Boolean ring, $x + x = 0$ for every $x$, and the ring is commutative. The ring $\mathbb{Z}/2\mathbb{Z}$ is a Boolean ring. The power set of a set is a Boolean ring, with symmetric difference as addition and intersection as multiplication. Each Boolean ring is a Boolean algebra with $x \wedge y = xy$, $x \vee y = x + y + xy$ and $\neg x = 1 + x$. This gives a correspondence between Boolean rings and Boolean algebras.