Algebra universalis

, 80:54 | Cite as

Distributive laws in residuated binars

  • Wesley FussnerEmail author
  • Peter Jipsen


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.


Residuated lattices Residuated binars Residuation Subvariety lattices 

Mathematics Subject Classification

06F05 03G10 08B15 



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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of DenverDenverUSA
  2. 2.Mathematics Chapman UniversityOrangeUSA

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