Geodesic
On Birkhoff's Problem 73 For Monoids
Canadian mathematical bulletin, Tome 3 (1960) no. 3, pp. 217-220

Voir la notice de l'article provenant de la source Cambridge University Press

Birkhoff in [2] poses the following problem:“Problem 73. Find necessary and sufficient conditions in order that the correspondence between the congruence relations and the (neutral) ideals of a lattice be one-one”.This problem has been solved by Areškin [l] and Hashimoto [3]. Essentially the conditions reduce to the r e quirement that the lattice be a generalized Boolean algebra. 
Brainerd, Barron. On Birkhoff's Problem 73 For Monoids. Canadian mathematical bulletin, Tome 3 (1960) no. 3, pp. 217-220. doi: 10.4153/CMB-1960-026-3
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[1] 1. Areškin, G. Ya., On congruence relations in distributive lattices with zero elements, Dokl. Akad, Nauk S.S.S.R. (NS), 90 (1953), 485-486. Google Scholar

[2] 2. Birkhoff, G., Lattice Theory, second edition, (New York, 1948.) Google Scholar

[3] 3. Hashimoto, J., Ideal theory for lattices, Math. Japon. 2 (1952), 149-186. Google Scholar

[4] 4. Preston, G. B., Inverse semi-groups, J. London Math. Soc. 29 (1954), 396-403. Google Scholar

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