Geodesic
Cantor property of quasi-unitary acts over completely (0-)simple semigroups
Dalʹnevostočnyj matematičeskij žurnal, Tome 23 (2023) no. 1, pp. 27-33.

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A universal algebra $A$ is called cantorian if for any algebra $B$ of the same signature, the existence of injective homomorphisms $A\to B$ and $B \to A$ implies an isomorphism of algebras $A$ and $B$. A right act $X$ over a semigroup $S$ is called quasiunitary if $X=XS$. We prove that every quasiunitary act over a completely simple semigroup and also every quasiunitary act with zero over a completely 0-simple semigroup are cantorian. 
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I. B. Kozhukhov; A. S. Sotov. Cantor property of quasi-unitary acts over completely (0-)simple semigroups. Dalʹnevostočnyj matematičeskij žurnal, Tome 23 (2023) no. 1, pp. 27-33. http://geodesic.mathdoc.fr/item/DVMG_2023_23_1_a3/

[1] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976 | MR

[2] A. S. Sotov, “Teorema Kantora – Bernshteina dlya poligonov nad gruppami”, Materialy VI Mezhd. konf. SITONI-2019, Izd-vo DonNTU, Donetsk, 2019, 120–123

[3] M. Kilp, U. Knauer, A. V. Mikhalev, Monoids, acts and categories, W. de Gruyter, Berlin – N.-Y., 2000 | MR | Zbl

[4] I. B. Kozhukhov, A. V. Mikhalev, “Poligony nad polugruppami.”, Fundamentalnaya i prikladnaya matematika, 23:3 (2020), 141–191

[5] A. Klifford, G. Preston, Algebraicheskaya teoriya polugrupp, v. 1, 2, Mir, M., 1987

[6] A. Yu. Avdeyev, I. B. Kozhukhov, “Acts over completely 0-simple semigroups”, Acta Cybernetica, 14:4 (2000), 523–531 | MR | Zbl

[7] I. B. Kozhukhov, A. O. Petrikov, “Proektivnye i in'ektivnye poligony nad vpolne prostymi polugruppami”, Fundamentalnaya i prikladnaya matematika, 21:1 (2016), 123–133 | MR

[8] I. B. Kozhukhov, A. O. Petrikov, “Proektivnye i in'ektivnye poligony nad vpolne 0-prostoi polugruppoi”, Chebyshevskii sb., 17:4 (2016), 65–78 | DOI | MR | Zbl