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On Hopfianity and Co-Hopfianity of Acts Over Groups

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Abstract

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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Authors and Affiliations

  1. National Research University of Electronic Technology, Moscow, Russia

    I. B. Kozhukhov

  2. Lomonosov Moscow State University, Moscow, Russia

    I. B. Kozhukhov & K. A. Kolesnikova

  3. Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia

    I. B. Kozhukhov & K. A. Kolesnikova

Authors
  1. I. B. Kozhukhov
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  2. K. A. Kolesnikova
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Correspondence to I. B. Kozhukhov.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 23, No. 3, pp. 131–139, 2020.

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Kozhukhov, I.B., Kolesnikova, K.A. On Hopfianity and Co-Hopfianity of Acts Over Groups. J Math Sci 269, 356–361 (2023). https://doi.org/10.1007/s10958-023-06286-4

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  • DOI: https://doi.org/10.1007/s10958-023-06286-4

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