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19-10-2019 | Foundations

A short note on divisible residuated semilattices

Author: Paolo Aglianò

Published in: Soft Computing | Issue 1/2020

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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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Title: A short note on divisible residuated semilattices
Author: Paolo Aglianò
Publication date: 19-10-2019
Publisher: Springer Berlin Heidelberg
Published in: Soft Computing / Issue 1/2020
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-019-04348-x

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