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.
Aglianò, P. (2020). A short note on divisible residuated semilattices. SOFT COMPUTING, 24(1), 259-266 [10.1007/s00500-019-04348-x].
A short note on divisible residuated semilattices
Aglianò, Paolo
2020-01-01
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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Utilizza questo identificativo per citare o creare un link a questo documento:
https://hdl.handle.net/11365/1082245