Minimal Varieties of Representable Commutative Residuated Lattices

0383374 - ÚI 2013 RIV NL eng J - Journal Article
Horčík, Rostislav
Minimal Varieties of Representable Commutative Residuated Lattices.
Studia Logica. Roč. 100, č. 6 (2012), s. 1063-1078. ISSN 0039-3215. E-ISSN 1572-8730
R&D Projects: GA ČR GAP202/10/1826
Institutional research plan: CEZ:AV0Z10300504
Keywords : commutative residuated lattice * subvariety lattice * minimal variety * substructural logic * maximally consistent logic
Subject RIV: BA - General Mathematics
Impact factor: 0.342, year: 2012

We solve several open problems on the cardinality of atoms in the subvariety lattice of residuated lattices and FL-algebras, we prove that the subvariety lattice of residuated lattices contains continuum many 4-potent commutative representable atoms. Analogous results apply also to atoms in the subvariety lattice of FLi-algebras and FLo-algebras. On the other hand, we show that the subvariety lattice of residuated lattices contains only five 3-potent commutative representable atoms and two integral commutative representable atoms. Inspired by the construction of atoms, we are also able to prove that the variety of integral commutative representable residuated lattices is generated by its 1-generated finite members.
Permanent Link: http://hdl.handle.net/11104/0213332