Boolean ring

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Noun[edit]

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.