Geodesic
Left regular bands of groups of left quotients
Glasgow mathematical journal, Tome 33 (1991) no. 1, pp. 29-40

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

In this paper we characterize semigroups S which have a semigroup Q of left quotients, where Q is an R-unipotent semigroup which is a band of groups. Recall that an R-unipotent (or left inverse) semigroup S is one in which every R-class contains a unique idempotent. It is well-known that any R-unipotent semigroup 5 is a regular semigroup in which the set of idempotents is a left regular band in that efe = ef for any idempotents e, fin S. R-unipotent semigroups were studied by several authors, see for example [1] and [13].Bailes [1]characterized R-unipotent semigroups which are bands of groups. This characterization extended the structure of inverse semigroups which are semilattices of groups. Recently, Gould studied in [7]the semigroup S which has a semigroup Q of left quotients where Q is an inverse semigroup which is a semilattice of groups. 
El-Qallali, Abdulsalam. Left regular bands of groups of left quotients. Glasgow mathematical journal, Tome 33 (1991) no. 1, pp. 29-40. doi: 10.1017/S0017089500008004
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