Abstract
In this note we prove that divisible residuated semilattices have some specific algebraic properties. We show that: (1) for normal and divisible residuated semilattices representability is equivalent to the existence of a join term, (2) any integral divisible residuated semilattice is distributive, and (3) a finite divisible residuated semilattice is integral and commutative.
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Aglianò, P. A short note on divisible residuated semilattices. Soft Comput 24, 259–266 (2020). https://doi.org/10.1007/s00500-019-04348-x
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DOI: https://doi.org/10.1007/s00500-019-04348-x