Cayley and Holland Theorems for Residuated Lattices

4 pages•Published: July 28, 2014

Abstract

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.

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.

Links:	https://easychair.org/publications/paper/FJfj
	https://doi.org/10.29007/gw6s

BibTeX entry

@inproceedings{TACL2013:Cayley_Holland_Theorems_Residuated,
  author    = {Nikolaos Galatos and Rostislav Horcik},
  title     = {Cayley and Holland Theorems for Residuated Lattices},
  booktitle = {TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic},
  editor    = {Nikolaos Galatos and Alexander Kurz and Constantine Tsinakis},
  series    = {EPiC Series in Computing},
  volume    = {25},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/FJfj},
  doi       = {10.29007/gw6s},
  pages     = {76-79},
  year      = {2014}}

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