Distributive laws in residuated binars
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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.
KeywordsResiduated lattices Residuated binars Residuation Subvariety lattices
Mathematics Subject Classification06F05 03G10 08B15
- 1.Blount, K.: On the Structure of Residuated Lattices. Ph.D. Dissertation, Vanderbilt University, Nashville (1999)Google Scholar
- 4.Fussner, W., Palmigiano, A.: Residuation algebras with functional duals. In: Adaricheva, K. et al. (eds.) Algebras and Lattices in Hawai’i: Honoring Ralph Freese, Bill Lampe, and J.B. Nation, Lulu, pp. 39–46 (2018)Google Scholar
- 5.Galatos, N., Jipsen, P., Kowalski, T., Ono, H.: Residuated lattices: an algebraic glimpse at substructural logics. In: Studies in Logic and the Foundations of Mathematics, vol. 151, pp. xxi+509. Elsevier (2007)Google Scholar