2019/01/20 by Chajda, Ivan, Länger, Helmut
#03B47 #06A11 #06B10 #06D15 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1901.06664
It is known that every relatively pseudocomplemented lattice is residuated and, moreover, it is distributive. Unfortunately, non-distributive lattices with a unary operation satisfying properties similar to relative pseudocomplementation cannot be converted in residuated ones. The aim of our paper is to introduce a more general concept of a relative residuated lattice in such a way that also non-modular sectionally pseudocomplemented lattices are included. We derive several properties of relative residuated lattices which are similar to those known for residuated ones and extend our results to posets.