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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     title = {On {Hopfianity} and {co-Hopfianity} of acts over groups},
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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/