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The failure of the amalgamation property for semilinear varieties of residuated lattices

In: Mathematica Slovaca, vol. 65, no. 4
José Gil-Férez - Antonio Ledda - Constantine Tsinakis
Detaily:
Rok, strany: 2015, 817 - 828
Kľúčové slová:
amalgamation property, residuated lattices, semilinear residuated lattices, lattice-ordered groups
O článku:
The amalgamation property $(AP)$ is of particular interest in the study of residuated lattices due to its relationship with various syntactic interpolation properties of substructural logics. There are no examples to date of non-commutative varieties of residuated lattices that satisfy the $AP$. The variety $\mathcal{S}em\mathcal{RL}$ of semilinear residuated lattices is a natural candidate for enjoying this property, since most varieties that have a manageable representation theory and satisfy the $AP$ are semilinear. However, we prove that this is not the case, and in the process we establish that the same is true for the variety $\mathcal{S}em\mathcal{C}an mathcal{RL}$ of semilinear cancellative residuated lattices. In addition, we prove that the variety whose members have a distributive lattice reduct and satisfy the identity $x(y\wedge z)w\eq xyw\wedge xzw$ also fails the $AP$.
Ako citovať:
ISO 690:
Gil-Férez, J., Ledda, A., Tsinakis, C. 2015. The failure of the amalgamation property for semilinear varieties of residuated lattices. In Mathematica Slovaca, vol. 65, no.4, pp. 817-828. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0057

APA:
Gil-Férez, J., Ledda, A., Tsinakis, C. (2015). The failure of the amalgamation property for semilinear varieties of residuated lattices. Mathematica Slovaca, 65(4), 817-828. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0057
O vydaní:
Publikované: 1. 8. 2015