Boolean ring

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English[edit]

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Etymology[edit]

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

Noun[edit]

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.