Geodesic
On semigroups whose nontrlvial left congruence classes are left ideals†
Glasgow mathematical journal, Tome 12 (1971) no. 1, pp. 1-5

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An equivalence relation δ on a semigroup S is called a left congruence of S if (u, v) Ε λ implies that (su, sv) Ε λ for every s in S. With every set L of pairwise disjoint left ideals (i. e. subsets L of S such that SL⊂EL), one can associate the left congruence {(u, v)|u = v or there exists an L in L such that u Ε L and v Ε L}. Thus every nonempty left ideal is a left congruence class (i. e. an equivalence class of some left congruence). A left congruence has the form just described if and only if all its nontrivial classes (i. e. its classes containing at least two elements) are left ideals. Such a left congruence is called a Rees left congruence if there is at most one nontrivial class. The identity relation on S is a Rees left congruence since the empty set is a left ideal by definition. 
Hotzel, E. On semigroups whose nontrlvial left congruence classes are left ideals†. Glasgow mathematical journal, Tome 12 (1971) no. 1, pp. 1-5. doi: 10.1017/S0017089500001051
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[1] 1.Clifford, A. H., Preston, G. B., The algebraic theory of semigroups, vol. I, Math. Surveys No. 7, Amer. Math. Soc. (Providence, R. I., 1961). Google Scholar

[2] 2.Hotzel, E., Halbgruppen mit ausschlieβlich Reesschen Linkskongruenzen, Math. Zeitschrift 112 (1969), 300–320. Google Scholar | DOI

[3] 3.Ljapin, E. S., Semisimple commutative associative systems (Russian), lzv. Akad. Nauk SSSR 14 (1950), 367–380. Google Scholar

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