In mathematics, a **Boolean ring** *R* is a ring for which *x*2 = *x* for all *x* in *R*; that is, *R* consists only of idempotent elements.

A Boolean ring is essentially the same thing as a Boolean algebra, with ring multiplication corresponding to conjunction or meet ∧, and ring addition to exclusive disjunction or symmetric difference (not disjunction ∨).

Read more about Boolean Ring: Notations, Examples, Relation To Boolean Algebras, Properties of Boolean Rings

### Famous quotes containing the word ring:

“Roll unmanly over this turning tuft,

O *ring* of seas, nor sorrow as I shift

From all my mortal lovers with a starboard smile....”

—Dylan Thomas (1914–1953)

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