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arXiv · 1810.00032

Orthomodular lattices can be converted into left residuated l-groupoids

Ivan Chajda·Helmut Länger
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Abstract

We show that every orthomodular lattice can be considered as a left residuated l-groupoid satisfying divisibility, antitony, the double negation law and three more additional conditions expressed in the language of residuated structures. Also conversely, every left residuated l-groupoid satisfying the mentioned conditions can be organized into an orthomodular lattice.

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Ivan Chajda, Helmut Länger. 2018-09-28. Orthomodular lattices can be converted into left residuated l-groupoids. https://doi.org/10.18514/mmn.2017.1730

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