# Boolean ring

## English

Wikipedia has an article on:

Wikipedia

### Noun

Boolean ring ‎(plural Boolean rings)

1. (algebra) A ring whose multiplicative operation is idempotent.
Let $\mathbb{Z}$ be the ring of integers and let $2\mathbb{Z}$ be its ideal of even integers. Then the quotient ring $\mathbb{Z} / 2\mathbb{Z}$ is a Boolean ring.
By Stone's Representation Theorem, the elements of a Boolean ring can be modeled as sets, with the additive operation corresponding to symmetric difference, and the multiplicative operation to set intersection.