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Boolean ring
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a Boolean ring <i>R</i> is a <a href="/facts/Ring_(mathematics)/JnCUXz63">ring</a> for which <i>x</i>2 = <i>x</i> for all <i>x</i> in <i>R</i>, that is, a ring that consists of only <a href="/facts/Idempotent_element_(ring_theory)/RE6AkdQd">idempotent elements</a>. An example is the ring of <a href="/facts/Modular_arithmetic/0wtRa5dU">integers modulo 2</a>. </p><p>Every Boolean ring gives rise to a <a href="/facts/Boolean_algebra_(structure)/cHbo65jm">Boolean algebra</a>, with ring multiplication corresponding to <a href="/facts/Logical_conjunction/62uyyn1d">conjunction</a> or <a href="/facts/Meet_(mathematics)/cYcLhRIR">meet</a> ∧, and ring addition to <a href="/facts/Exclusive_or/FHyr7hGQ">exclusive disjunction</a> or <a href="/facts/Symmetric_difference/W2QST1Qr">symmetric difference</a> (not <a href="/facts/Logical_disjunction/jbI2EGlM">disjunction</a> ∨, which would constitute a <a href="/facts/Semiring/7cSvWXVQ">semiring</a>). Conversely, every Boolean algebra gives rise to a Boolean ring. Boolean rings are named after the founder of Boolean algebra, <a href="/facts/George_Boole/fWJT2rek">George Boole</a>. </p>