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are at least four different and incompatible systems of notation for Boolean rings and algebras:
* In commutative algebra the standard notation is to use for the ring sum of and , and use for their product.
* In logic, a common notation is to use for the meet (same as the ring product) and use for the join, given in terms of ring notation (given just above) by .
* In set theory and logic it is also common

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