The following problem is considered: when can the action of a cancellative semigroup $S$ on a set be extended to a simply transitive action of the universal group of $S$ on a larger set.
@article{119397, author = {Pierre Antoine Grillet}, title = {Cancellative actions}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {44}, year = {2003}, pages = {399-411}, zbl = {1101.20033}, mrnumber = {2025809}, language = {en}, url = {http://dml.mathdoc.fr/item/119397} }
Grillet, Pierre Antoine. Cancellative actions. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) pp. 399-411. http://gdmltest.u-ga.fr/item/119397/
Theory of greatest decompositions of semigroups (a survey), Filomat (Nis) 9:3 (1995), 385-426. (1995) | MR 1385929 | Zbl 0848.20054
Contribution à la théorie des demi-groupes, II, Rend. Mat. Appl. 10 (1951), 183-200. (1951) | MR 0048426 | Zbl 0045.00802
Automata, Languages, and Machines, Vol. B, Academic Press, 1976. | MR 0530383 | Zbl 0359.94067
Cancellative coextensions, to appear in Acta Sci. Math. (Szeged). | MR 2034193 | Zbl 1053.20055
Flatness and localization over monoids, Math. Nachr. 48 (1971), 315-334. (1971) | MR 0296191