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**ymar** Is there a name for an algrebraic structure with two operations, addition and multiplication, such that

1) the additive structure is that of a commutative monoid;

2) the multiplicative structue is that of a monoid;

3) multiplication distributes over addition?

A simple example would be any power set with the operations $\displaystyle \cup$ and $\displaystyle \cap$, but also the set of all binary relations on a set with the operations $\displaystyle \cup$ and $\displaystyle \circ$, the latter being the composition of relations.