Abstract
It is known that there are only two cancellative atoms in the subvariety lattice of residuated lattices, namely the variety of Abelian ℓ-groups \({\mathcal{CLG}}\) generated by the additive ℓ-group of integers and the variety \({\mathcal{CLG}^-}\) 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 \({\mathcal{CLG}^-}\). This proves that there are infinitely many covers above \({\mathcal{CLG}^-}\) which are commutative, integral, and representable.
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Presented by C. Tsinakis.
The work of the author was partly supported by the grant KJB100300701 of the Grant Agency of the Academy of Sciences of the Czech Republic and partly by the Institutional Research Plan AV0Z10300504.
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Horčík, R. Cancellative residuated lattices arising on 2-generated submonoids of natural numbers. Algebra Univers. 63, 261–274 (2010). https://doi.org/10.1007/s00012-010-0076-1
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DOI: https://doi.org/10.1007/s00012-010-0076-1