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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Fussner, W., Jipsen, P. Distributive laws in residuated binars. Algebra Univers. 80, 54 (2019). https://doi.org/10.1007/s00012-019-0625-1
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DOI: https://doi.org/10.1007/s00012-019-0625-1