  It is an easy observation that every residuated lattice is in fact a semiring
because multiplication distributes over join and the other axioms of a semiring
are satisfied trivially. This semiring is commutative, idempotent and simple.
The natural question arises if the converse assertion is also true. We show
that the conversion is possible provided the given semiring is, moreover,
completely distributive. We characterize semirings associated to complete
residuated lattices satisfying the double negation law where the assumption of
complete distributivity can be omitted. A similar result is obtained for
idempotent residuated lattices.
