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arXiv · 1901.01615

Distributive laws in residuated binars

Wesley Fussner·Peter Jipsen
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Abstract

In residuated binars there are six non-obvious distributivity identities of $\cdot$,$/$,$\backslash$ over $\wedge, \vee$. We show that in residuated binars with distributive lattice reducts there are some dependencies among these identities; specifically, there are six pairs of identities that imply another one of these identities, and we provide counterexamples to show that no other dependencies exist among these.

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Wesley Fussner, Peter Jipsen. 2019-01-06. Distributive laws in residuated binars. https://doi.org/10.1007/s00012-019-0625-1

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