Geodesic
On Hopfianity and co-Hopfianity of acts over groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 3, pp. 131-139.

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A universal algebra is called Hopfian if any of its surjective endomorphisms is an automorphism, and co-Hopfian if injective endomorphisms are automorphisms. In this paper, necessary and sufficient conditions are found for Hopfianity and co-Hopfianity of unitary acts over groups. It is proved that a coproduct of finitely many acts (not necessarily unitary) over a group is Hopfian if and only if every factor is Hopfian. 
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I. B. Kozhukhov; K. A. Kolesnikova. On Hopfianity and co-Hopfianity of acts over groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 3, pp. 131-139. http://geodesic.mathdoc.fr/item/FPM_2020_23_3_a8/

[1] Kartashov V. K., “Nezavisimye sistemy porozhdayuschikh i svoistvo Khopfa dlya unarnykh algebr”, Diskret. matem., 20:4 (2008), 79–84 | Zbl

[2] Kurosh A. G., Teoriya grupp, Nauka, M., 1967 | MR

[3] Maksimovskii M. Yu., “O bipoligonakh i multipoligonakh nad polugruppami”, Matem. zametki, 87:6 (2010), 855–866 | MR

[4] Kilp M., Knauer U., Mikhalev A. V., Monoids, acts and categories, Walter de Gruyter, Berlin, 2000 | MR | Zbl