Cayley’s and Holland’s Theorems for Idempotent Semirings and Their Applications to Residuated Lattices

Authors: N. Galatos, Rostislav Horčík
Publication year: 2013
Publication type: Článek v odborném periodiku
Periodical: Semigroup Forum
Projects: Algebraic Methods in Proof Theory
Bibliographic citation: GALATOS, N., HORČÍK, Rostislav. Cayley’s and Holland’s Theorems for Idempotent Semirings and Their Applications to Residuated Lattices. Semigroup Forum. 2013, 87(3), 569-589. ISSN 0037-1912. E-ISSN 1432-2137
Dostupné z: doi:10.1007/s00233-013-9513-8
DOI: 10.1007/s00233-013-9513-8
ID: 395570

Abstract

We extend Cayley’s and Holland’s representation theorems to idempotent semirings and residuated lattices, and provide both functional and relational versions. Our analysis allows for extensions of the results to situations where conditions are imposed on the order relation of the representing structures. Moreover, we give a new proof of the finite embeddability property for the variety of integral residuated lattices and many of its subvarieties.