2018/12/22 by Ivan Chajda, Chajda, Ivan, Helmut Länger +1 · 1 citation
Computer Science · Decision Sciences · Mathematics · #06A11 #06C05 #06C15 #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Logic (math.LO) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1812.09491
openalex publication_date 2018/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.