Distributive laws in residuated binars

Distributive laws in residuated binars

In residuated binars there are six non-obvious distributivity identities of · , / , \ over ∧ , ∨ . 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 i...

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Veröffentlicht in:Algebra universalis 2019-12, Vol.80 (4), p.1-13, Article 54
Hauptverfasser: Fussner, Wesley, Jipsen, Peter
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Mathematics and Statistics
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description In residuated binars there are six non-obvious distributivity identities of · , / , \ over ∧ , ∨ . 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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subjects Algebra
Mathematics
Mathematics and Statistics
title Distributive laws in residuated binars
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