Cancellative Residuated Lattices Arising on 2-Generated Submonoids of Natural Numbers

0348399 - ÚI 2011 RIV CH eng J - Journal Article
Horčík, Rostislav
Cancellative Residuated Lattices Arising on 2-Generated Submonoids of Natural Numbers.
Algebra Universalis. Roč. 63, 2-3 (2010), s. 261-274. ISSN 0002-5240. E-ISSN 1420-8911
R&D Projects: GA AV ČR KJB100300701
Institutional research plan: CEZ:AV0Z10300504
Keywords : residuated lattice * cancellative commutative residuated lattice * subvariety lattice * submonoid of natural numbers
Subject RIV: BA - General Mathematics
Impact factor: 0.479, year: 2010

It is known that there are only two cancellative atoms in the subvariety lattice of residuated lattices, namely the variety of Abelian l-groups generated by the additive l-group of integers and the variety V generated by the negative cone of this l-group. In this paper we consider all cancellative residuated chains arising on 2-generated submonoids of natural numbers and show that almost all of them generate a cover of V. This proves that there are infinitely many covers above V which are commutative, integral, and representable.
Permanent Link: http://hdl.handle.net/11104/0188946