Geodesic
Translational hull and semigroups of binary relations
Glasgow mathematical journal, Tome 9 (1968) no. 1, pp. 12-21

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

Various semigroups of partial transformations (and more generally, semigroups of binary relations) on a set have been studied by a number of Soviet mathematicians; to mention only a few: Gluskin [2], Ljapin [4], Shutov [6], Zaretski [7], [8]. In their study the densely embedded ideal of a semigroup introduced by Ljapin [4] plays a central role. In fact, a concrete semigrou Q is described in several instances by its abstract characteristic, namely either by a set of postulates on an abstract semigroup or by a set of postulates (which are usually much simpler) on an abstract semigroup S which is a densely embedded ideal of a semigroup T isomorphic to Q. In many cases, the densely embedded ideal S is a completely 0-simple semigroup. The following theorem [3, 1.7.1] reduces the study of a semigroup Q with a weakly reductive densely embedded ideal S to the study of the translational hull of S:Theorem (Gluskin). If S is a weakly reductive densely embedded ideal of a semigroup Q, then Q is isomorphic to the translational hull ω(S) of S. 
Petrich, Mario. Translational hull and semigroups of binary relations. Glasgow mathematical journal, Tome 9 (1968) no. 1, pp. 12-21. doi: 10.1017/S0017089500000240
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