Residuated Multilattices: a First Glimpse into Their Structures
نویسنده
چکیده
We prove that when divisibility is added to a residuated multilattice, this causes the multilattice structure to collapse down to a residuated lattice. This motivates the study of semi-divisibility and regularity on residuated multilattices. The ordinal sum construction is also applied to residuated multilattices as a way to construct new examples of both residuated multilattices and consistent filters. Finally, it is also established that the smallest residuated multilattice that is not a residuated lattice has order 7.
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