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Added as examples: , and with . Proved that they are exactly the boolean rigs of cardinal less or equal than .
I don’t know if boolean rigs in the sense of this entry are always commutative. In The variety of Boolean semirings, they show that they are commutative assuming that . If some noncommutative boolean rig exists, it must be of cardinal , not be a ring (because boolean rings are commutative) and not verify this equation.
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