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 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | 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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ISSN: | 0002-5240 1420-8911 |
DOI: | 10.1007/s00012-019-0625-1 |