English

Noun

Boolean ring ‎(plural Boolean rings)

1. (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.