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

0395570 - ÚI 2014 RIV US eng J - Journal Article
Galatos, N. - Horčík, Rostislav
Cayley’s and Holland’s Theorems for Idempotent Semirings and Their Applications to Residuated Lattices.
Semigroup Forum. Roč. 87, č. 3 (2013), s. 569-589. ISSN 0037-1912. E-ISSN 1432-2137
R&D Projects: GA ČR GAP202/11/1632
Institutional research plan: CEZ:AV0Z1030915
Institutional support: RVO:67985807
Keywords : residuated lattice * idempotent semiring * conucleus * Cayley * Holland * representation theorem
Subject RIV: BA - General Mathematics
Impact factor: 0.384, year: 2013

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.
Permanent Link: http://hdl.handle.net/11104/0223574