Geodesic
Permutability of Semilattice Congruences on Lattices
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 370-375

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Many authors have studied lattice congruences on lattices, but it seems that there are few studies concerning semilattice congruences on lattices. However, it seems that the semilattice congruences on lattices are closely connected with their structure. In this paper, we shall study the characterizations of modular, distributive, and relatively complemented lattices by the permutability of semilattice congruences.We can obtain the dual statements of the following discussion, but we shall not write them as a rule to avoid double descriptions. 
Fujiwara, Tsuyoshi. Permutability of Semilattice Congruences on Lattices. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 370-375. doi: 10.4153/CJM-1967-029-1
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[1] 1. Dilworth, R. P., The structure of relatively complemented lattices, Ann. Math., 51 (1950), 348–359. Google Scholar

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