Geodesic
Complements in the lattice of congruences
Sbornik. Mathematics, Tome 17 (1972) no. 1, pp. 148-181 
L. A. Skornyakov. Complements in the lattice of congruences. Sbornik. Mathematics, Tome 17 (1972) no. 1, pp. 148-181. http://geodesic.mathdoc.fr/item/SM_1972_17_1_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Several theorems are proved concerning the structure of universal algebras whose lattice of congruences is complemented. Among the corollaries are the semigroup results of Grappy. Under rather weak supplementary conditions it is established that the existence of complements in the lattice of congruences implies, both for the algebra itself and all its factor algebras, distributivity of these lattices. Bibliography: 6 titles.

[1] P. Kon, Universalnaya algebra, Mir, Moskva, 1968 | MR

[2] A. G. Kurosh, Lektsii po obschei algebre, Fizmatgiz, Moskva, 1962 | MR

[3] J. Grappy, “Sur les demi-groupes admettant un certain type de treillis de congruences”, C. r. Acad. Sci., 256:14 (1963), 2980–2982 | MR | Zbl

[4] J. Grappy, “Demi-groupes dont le treillis des congruences est un treillis complémenté”, Sém. Dubreil et Pisot. Fac. Sci. Paris, 1963–1964, 17 (1967), 21/01–21/21

[5] E. J. Tully, “Semigroups in which each ideal is a retract”, J. Austral. Math. Soc, 9:1–2 (1969), 239–245 | DOI | MR | Zbl

[6] J. Varlet, “Congruences dans les demi-lattis”, Bull. Soc. Roy. Sci. Liege, 34:5–6 (1965), 231–240 | MR | Zbl