It has been proved by J贸nsson (1953) that the modular law holds in the lattice of commuting equivalence relations. We give some necessary and sufficient conditions for the distributive law and its dual to hold for commuting equivalence relations....
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A lattice L is weakly atomic if, given x<y in L, there exist a,b∈L such that x⩽a≺b⩽y, where ≺ denotes the covering relation of L. A complete lattice L satisfies the join-infinite distributive law if for any S⊆L and x∈L,(JID)x∧(⋁S)=⋁{x∧y|y∈S}. Th...
A., Representation of Hilbert algebras and implicative semilattices, Central European Journal of Mathematics, 2003, 4, 561-572 10.2478/BF02475182Search in Google Scholar [7] Chajda I., Halaš R. and Kühr J., Semilattice Structures. Heldermann Verlag, Research and Exposition in Mathematics, 30...
generalized distributive lawThe previous paper was concerned with systems of equations over a certain family of quasigroups. In that work a method of elimination of an outermost variable from the system of equations was suggested and it was shown that further elimination of variables requires that ...