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

0395570 - ÚI 2014 RIV US eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR GAP202/11/1632
Výzkumný záměr: CEZ:AV0Z1030915
Institucionální podpora: RVO:67985807
Klíčová slova: residuated lattice * idempotent semiring * conucleus * Cayley * Holland * representation theorem
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.384, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0223574