Download PDFOpen PDF in browserCayley and Holland Theorems for Residuated Lattices4 pages•Published: July 28, 2014AbstractWe 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.Keyphrases: cayley, holland, idempotent semimodule, idempotent semiring, representation, residuated lattice In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 76-79.
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