Chajda, I., & Länger, H. (2023). Operator residuation in orthomodular posets of finite height. Fuzzy Sets and Systems, 467, Article 108589. https://doi.org/10.1016/j.fss.2023.108589
E104-01 - Forschungsbereich Algebra E104 - Institut für Diskrete Mathematik und Geometrie
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Journal:
Fuzzy Sets and Systems
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ISSN:
0165-0114
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Date (published):
15-Sep-2023
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Number of Pages:
11
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Publisher:
ELSEVIER
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Peer reviewed:
Yes
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Keywords:
orthomodular poset; weakly orthomodular poset; dually weakly orthomodular poset; poset of finite height; operator residuated structure; left adjointness
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Abstract:
We show that for every orthomodular poset of finite height there can be defined two operators forming an adjoint pair with respect to an order-like relation defined on the power set of P. This enables us to introduce the so-called operator residuated poset corresponding to P from which the original orthomodular poset P can be recovered. We show that this construction of operators can be applied also to so-called weakly orthomodular and dually weakly orthomodular posets. Examples of such posets are included.
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Project title:
Die vielen Facetten der Orthomodularität: I 4579-N (FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
CC BY 4.0
