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Lattices in quasiordered sets. (English) Zbl 0773.06002
Let \(Q\) be a quasiorder on a set \(A\). It is shown that the factor set \(A/Q\cap Q^{-1}\) ordered by the induced order is a lattice if and only if \(A\) can be equipped with two binary operations satisfying a set of identities, similar to those for lattices, and determining the quasiorder \(Q\).
Reviewer: J.Niederle (Brno)

06A06 Partial orders, general
Full Text: EuDML
[1] Chajda I., Haviar M.: Induced pseudoorders. Acta UPO, Fac. rer. nat. 100 (1991), 9-16. · Zbl 0772.04001 · eudml:23528
[2] Fried E.: Tournaments and non-associative lattices. Ann. Univ. Sci. Budapest, sectio Math. 13 (1970), 151-164. · Zbl 0224.06004
[3] Leutola K., Nieminen J.: Posets and generalized lattices. Algebra Univ. 16 (1983), 344-354. · Zbl 0514.06003 · doi:10.1007/BF01191789
[4] Nieminen J.: On \(\chi_{\text{sub}}\)-lattices and convex substructures of lattices and semilattices. Acta Math. Hung., 44 (1984), 229-236. · Zbl 0567.06006 · doi:10.1007/BF01950275
[5] Nieminen J.: On distributive and modular \(\chi\)-lattices. Yokohama Math. J., 31 (1983), 13-20. · Zbl 0532.06002
[6] Skala H.L.: Trellis theory. Algebra Univ. 1 (1971), 218-233. · Zbl 0242.06003 · doi:10.1007/BF02944982
[7] Snášel V.: Theory of \(\lambda\)-lattices. Thesis, Palacký University Olomouc, 1990.
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