Geodesic
The lattice of congruences on a band of groups
Glasgow mathematical journal, Tome 14 (1973) no. 2, pp. 187-197

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

It is implicit in a result of Kapp and Schneider [3] that, if Sisa completely simple semigroup, then the lattice Λ(S) of congruences on S can be embedded in the product of certain sublattices. In this paper we consider the problem of embedding Λ(S) in a product of sublattices, when S is an arbitrary band of groups. The principal tool is the θ-relation of Reilly and Scheiblich [7]. The class of θ-modular bands of groups is definedby means of a type of modularity condition on Λ(S). It is shown that the θ-modular bands of groups are precisely those for which a certain function is an embedding of Λ(S) into a product of sublattices. The problem of embedding the inverse semigroup congruences into a certain product lattice is also considered. 
Spitznagel, C. The lattice of congruences on a band of groups. Glasgow mathematical journal, Tome 14 (1973) no. 2, pp. 187-197. doi: 10.1017/S0017089500001956
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