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Relatively residuated lattices and posets

In: Mathematica Slovaca, vol. 70, no. 2
Ivan Chajda - Jan Kühr - Helmut Länger

Details:

Year, pages: 2020, 239 - 250
Keywords:
relatively residuated lattice, relatively operator residuated poset, sectionally pseudocomplemented lattice, sectionally pseudocomplemented poset
About article:
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.
How to cite:
ISO 690:
Chajda, I., Kühr, J., Länger, H. 2020. Relatively residuated lattices and posets. In Mathematica Slovaca, vol. 70, no.2, pp. 239-250. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0347

APA:
Chajda, I., Kühr, J., Länger, H. (2020). Relatively residuated lattices and posets. Mathematica Slovaca, 70(2), 239-250. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0347
About edition:
Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Published: 10. 3. 2020