Definition:Boolean Ring

Definition
Let $\left({R, +, \circ}\right)$ be a ring.

Then $R$ is called a Boolean ring iff $R$ is an idempotent ring with unity.

Boolean Ring Axioms
More abstractly, a Boolean ring is an algebraic structure $\left({R, *, \circ}\right)$ subject to the following axioms:

Also defined as
Some sources use the (deprecated) name Boolean ring to mean what is better known as a Boolean algebra.

Others define it simply to mean what we have called an idempotent ring, not imposing that it have a unity.

Also see

 * Definition:Boolean Algebra