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Fundamentalnaya i Prikladnaya Matematika, 2020, Volume 23, Issue 3, Pages 131–139 (Mi fpm1901)  
This article is cited in 2 scientific papers (total in 2 papers)

On Hopfianity and co-Hopfianity of acts over groups

I. B. Kozhukhovabc, K. A. Kolesnikovabc

a National Research University of Electronic Technology, Moscow, Russia
b Lomonosov Moscow State University, Moscow, Russia
c Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia
Full-text PDF (131 kB) Citations (2)
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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.
Funding agency Grant number
Moscow Center of Fundamental and Applied Mathematics
This research was supported by a grant of the Moscow Center of Fundamental and Applied Mathematics of MSU.
English version:
Journal of Mathematical Sciences (New York), 2023, Volume 269, Issue 3, Pages 356–361
DOI: https://doi.org/10.1007/s10958-023-06286-4
Document Type: Article
UDC: 512.534.3
Language: Russian
Citation: I. B. Kozhukhov, K. A. Kolesnikova, “On Hopfianity and co-Hopfianity of acts over groups”, Fundam. Prikl. Mat., 23:3 (2020), 131–139; J. Math. Sci., 269:3 (2023), 356–361
Citation in format AMSBIB
\Bibitem{KozKol20}
\by I.~B.~Kozhukhov, K.~A.~Kolesnikova
\paper On Hopfianity and co-Hopfianity of acts over groups
\jour Fundam. Prikl. Mat.
\yr 2020
\vol 23
\issue 3
\pages 131--139
\mathnet{http://mi.mathnet.ru/fpm1901}
\transl
\jour J. Math. Sci.
\yr 2023
\vol 269
\issue 3
\pages 356--361
\crossref{https://doi.org/10.1007/s10958-023-06286-4}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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