# Boolean ring

## English[edit]

### Etymology[edit]

Named after George Boole (1815–1864), an English mathematician, educator, philosopher and logician.

### Noun[edit]

**Boolean ring** (*plural* **Boolean rings**)

- (algebra) A ring whose multiplicative operation is idempotent.
- Let be the ring of integers and let be its ideal of even integers. Then the quotient ring 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.

- Let be the ring of integers and let be its ideal of even integers. Then the quotient ring is a