Abstract
Residuated structures derived from commutative idempotent semirings
Highlights
Since the reduct of every residuated lattice is a semiring, we can ask under what condition a semiring can be converted into a residuated lattice
It turns out that this is possible if the semiring in question is commutative, idempotent, G-simple and equipped with an antitone involution
If the mentioned semiring is finite it can be converted into a residuated lattice or join-semilattice without asking an antitone involution on it
Summary
Since the reduct of every residuated lattice is a semiring, we can ask under what condition a semiring can be converted into a residuated lattice.
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