Geodesic
Two examples of diagonal bi-acts
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 3, pp. 3-9 
T. V. Apraksina; I. Barkov; I. B. Kozhukhov. Two examples of diagonal bi-acts. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 3, pp. 3-9. http://geodesic.mathdoc.fr/item/FPM_2013_18_3_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

An example of a right cancellative semigroup is constructed such that the diagonal bi-act of this semigroup is cyclic. Moreover, it is proved that every semigroup can be isomorphically embedded into a semigroup such that its diagonal bi-act of second order is cyclic, but the diagonal bi-act of third order is not finitely generated.

[1] Gallagher P., “On the finite and non-finite generation of diagonal acts”, Commun. Algebra, 34 (2006), 3123–3137 | DOI | MR | Zbl

[2] Gallagher P., Rus̆kuc N., “Generation of diagonal acts of some semigroups of transformations and relations”, Bull. Austral. Math. Soc., 72 (2005), 139–146 | DOI | MR | Zbl

[3] Kilp M., Knauer U., Mikhalev A. V., Monoids, Acts and Categories, Walter de Gruyter, Berlin, 2000 | MR | Zbl