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Mathematics > Logic

arXiv:1812.09491 (math)
[Submitted on 22 Dec 2018]

Title:Residuation in modular lattices and posets

Authors:Ivan Chajda, Helmut Länger
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Abstract:We show that every complemented modular lattice can be converted into a left residuated lattice where the binary operations of multiplication and residuum are term operations. The concept of an operator left residuated poset was introduced by the authors recently. We show that every strongly modular poset with complementation as well as every strictly modular poset with complementation can be organized into an operator left residuated poset in such a way that the corresponding operators M(x,y) and R(x,y) can be expressed by means of the operators L and U in posets. We describe connections between the operator left residuation in these posets and the residuation in their lattice completion. We also present examples of strongly modular and strictly modular posets.
Subjects: Logic (math.LO)
MSC classes: 06A11, 06C15, 06C05
Cite as: arXiv:1812.09491 [math.LO]
  (or arXiv:1812.09491v1 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.1812.09491

Submission history

From: Helmut Länger [view email]
[v1] Sat, 22 Dec 2018 10:04:42 UTC (7 KB)
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