Algebra universalis

, Volume 63, Issue 2–3, pp 261–274 | Cite as

Cancellative residuated lattices arising on 2-generated submonoids of natural numbers

  • Rostislav Horčík


It is known that there are only two cancellative atoms in the subvariety lattice of residuated lattices, namely the variety of Abelian -groups \({\mathcal{CLG}}\) generated by the additive -group of integers and the variety \({\mathcal{CLG}^-}\) generated by the negative cone of this -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 \({\mathcal{CLG}^-}\). This proves that there are infinitely many covers above \({\mathcal{CLG}^-}\) which are commutative, integral, and representable.

2000 Mathematics Subject Classification

Primary: 06F05 Secondary: 20M14 

Keywords and phrases

residuated lattice cancellative commutative residuated lattice subvariety lattice submonoid of natural numbers 


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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Institute of Computer ScienceAcademy of Sciences of the Czech RepublicPrague 8Czech Republic
  2. 2.Department of Mathematics, Faculty of Electrical EngineeringCzech Technical University in PraguePrague 6Czech Republic

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