Cayley and Holland Theorems for Residuated Lattices
Nikolaos Galatos, Rostislav Horčı́k · EPiC series in computing · 2018
We obtain representation theorems for residuated lattices. The representing structure consists of special self maps on an ordered set. We prove two types of theorems; one that generalizes Cayley's theorem for groups/monoids and one (for special residuated lattices) that generalizes Holland's theorem for lattice-ordered groups. Our results are presented in the language of idempotent semirings and semimodules, and they are first established for these types of structures.