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Algebra in which we consider a set S and two commutative
operations + and ×, with the rules that:

1. each of the operations has an identity element in S, and these
   elements are not the same;
   
2. each operation is distributive over the other;
   
3. each element has an inverse in S under each of the operations.
   

Note that the operations + and × are not quite the same as for the ordinary numbers.
This kind of algebra is widely used in logic and set theory.