Geodesic
Congruences on an orthodox semigroup via the minimum inverse semigroup congruence
Glasgow mathematical journal, Tome 18 (1977) no. 2, pp. 181-192

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It is well known that the lattice Λ(S) of congruences on a regular semigroup S contains certain fundamental congruences. For example there is always a minimum band congruence β, which Spitznagel has used in his study of the lattice of congruences on a band of groups [16]. Of key importance to his investigation is the fact that β separates congruences on a band of groups in the sense that two congruences are the same if they have the same meet and join with β. This result enabled him to characterize θ-modular bands of groups as precisely those bands of groups for which ρ⃗(ρ∨β, ρ∧β)is an embedding of Λ(S) into a product of sublattices. 
Eberhart, Carl; Williams, Wiley. Congruences on an orthodox semigroup via the minimum inverse semigroup congruence. Glasgow mathematical journal, Tome 18 (1977) no. 2, pp. 181-192. doi: 10.1017/S0017089500003256
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Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vols. 1 and 2, Amer. Math. Soc. Mathematical Surveys No. 7 (Providence, R.I., 1961, 1967). Google Scholar

Green, D. G., The lattice of congruences on an inverse semigroup, Pacific J. Math. 57 (1975), 141–152. Google Scholar | DOI

Hall, T. E., On regular semigroups whose idempotents form a subsemigroup. Bull. Austral. Math. Soc. 1 (1969), 195–208. Google Scholar | DOI

Hall, T. E., On the lattice of congruences on a regular semigroup, Bull. Austral. Math. Soc. 1 (1969), 231–235. Google Scholar | DOI

Howie, J. M., Naturally ordered bands, Glasgow Math. J. 8 (1967), 55–58. Google Scholar | DOI

Howie, J. M., The maximum idempotent-separating congruence on an inverse semigroup, Proc. Edinburgh Math. Soc. (2) 14 (1964–5), 71–79. Google Scholar | DOI

Howie, J. M. and Lallement, G., Certain fundamental congruences on a regular semigroup, Proc. Glasgow Math. Assoc. 7 (1966), 145–159. Google Scholar | DOI

Kapp, K. M. and Schneider, H., Completely 0-simple semigroups (New York, 1969). Google Scholar

Lallement, G., Congruences et equivalences de Green sur un demi-groupe regulier, C. R. Acad. Sci. Sér A, 262 (1966), 613–616. Google Scholar

Meakin, J., Congruences on orthodox semigroups, J. Austral. Math. Soc. 12 (1971), 323–341. Google Scholar

Munn, W. D., A certain sublattice of the lattice of congruences on a regular semigroup, Proc. Cambridge Philos. Soc. 60 (1964), 385–391. Google Scholar

Preston, G. B., Congruences on completely simple semigroups, Proc. London Math. Soc. (3) 11 (1961), 557–576. Google Scholar | DOI

Reilly, N. R. and Scheiblich, H. E., Congruences on regular semigroups, Pacific J. Math. 23 (1967), 349–360. Google Scholar | DOI

Scheiblich, H. E., Certain congruence and quotient lattices related to completely 0-simple and primitive regular semigroups, Glasgow Math. J. 10 (1969), 21–24. Google Scholar

Scheiblich, H. E., Kernels of inverse semigroup homomorphisms, J. Austral. Math. Soc. 18 (1974), 289–292. Google Scholar

Spitznagel, C., The lattice of congruences on a band of groups, Glasgow Math. J. 14 (1973), 187–197. Google Scholar | DOI

Spitznagel, C., θ-modular bands of groups, Trans. Amer. Math. Soc. 177 (1973), 469–482. Google Scholar

Fergenbaum, Ruth, Kernels of orthodox semigroup homomorphisms, J. Austral. Math. Soc. Ser. A 22 (1976), 234–245. Google Scholar

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