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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