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Relatively residuated lattices and posets

Ivan Chajda, Jan Kühr and Helmut Länger
From the journal Mathematica Slovaca

Abstract

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 relatively residuated lattice in such a way that also non-modular sectionally pseudocomplemented lattices are included. We derive several properties of relatively residuated lattices which are similar to those known for residuated ones and extend our results to posets.

  1. Communicated by Mirko Navara

Acknowledgement

We thank the anonymous referee for his/her valuable suggestions.

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Received: 2019-01-20
Accepted: 2019-10-09
Published Online: 2020-03-10
Published in Print: 2020-04-28

© 2020 Mathematical Institute Slovak Academy of Sciences