Weakly associative lattices and tolerance relations
Ivan Chajda, Bohdan Zelinka · Czechoslovak Mathematical Journal · 1976
The investigation of tolerance relations has been rather expansive in a few last years.A number of results in this theory show its principal role in various branches of algebra and its applications (for example tolerance spaces, graph theory, topology etc.).In the paper [10] some results on the existence of non-trivial compatible tolerance relations on lattices were derived.Some of them can be generalized to weakly associative lattices and these "generalized" lattices offer a new view of these problems.A weakly associative lattice is obtained, roughly speaking, if the transitivity of the lattice ordering is omitted.These algebraic structures have very interesting properties and many of their applications play a principal role in algebra as is shown in the papers [1], [2], [3], [4], [5].The purpose of this paper is to establish some results on the existence and basic properties of tolerance relations compatible with weakly associative lattices and tournaments.