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Diskr. Mat., 2008, Volume 20, Issue 4, Pages 79–84 (Mi dm1027)  

This article is cited in 4 scientific papers (total in 4 papers)

Independent systems of generators and the Hopf property for unary algebras

V. K. Kartashov


Abstract: We introduce the notion of an independent set of elements of a unary algebra as a subset of its support, where in any pair of elements one element does not belong to the subalgebra generated by the other. It is proved that any two independent systems of generators of a unary algebra have the same cardinality. With the use of this assertion it is proved that any finitely generated unary algebra with commutative operations possesses the Hopf property: each epiendomorphism of the algebra is an automorphism.

DOI: https://doi.org/10.4213/dm1027

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English version:
Discrete Mathematics and Applications, 2008, 18:6, 625–630

Bibliographic databases:

UDC: 512.62
Received: 25.04.2007

Citation: V. K. Kartashov, “Independent systems of generators and the Hopf property for unary algebras”, Diskr. Mat., 20:4 (2008), 79–84; Discrete Math. Appl., 18:6 (2008), 625–630

Citation in format AMSBIB
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\by V.~K.~Kartashov
\paper Independent systems of generators and the Hopf property for unary algebras
\jour Diskr. Mat.
\yr 2008
\vol 20
\issue 4
\pages 79--84
\mathnet{http://mi.mathnet.ru/dm1027}
\crossref{https://doi.org/10.4213/dm1027}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2500605}
\zmath{https://zbmath.org/?q=an:1175.08001}
\elib{http://elibrary.ru/item.asp?id=20730267}
\transl
\jour Discrete Math. Appl.
\yr 2008
\vol 18
\issue 6
\pages 625--630
\crossref{https://doi.org/10.1515/DMA.2008.047}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-57349190215}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. K. Kartashov, “O nekotorykh rezultatakh i nereshennykh zadachakh teorii unarnykh algebr”, Chebyshevskii sb., 12:2 (2011), 18–26  mathnet  mathscinet
    2. V. K. Kartashov, A. V. Kartashova, V. N. Ponomarev, “Ob usloviyakh distributivnosti i modulyarnosti reshetok kongruentsii kommutativnykh unarnykh algebr”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 13:4(2) (2013), 52–57  mathnet  crossref
    3. A. V. Kartashova, “On Commutative Unary Algebras with Totally Ordered Congruence Lattice”, Math. Notes, 95:1 (2014), 67–77  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. Apraksina T.V., Barkov I.V., Kozhukhov I.B., “Diagonal Ranks of Semigroups”, Semigr. Forum, 90:2 (2015), 386–400  crossref  mathscinet  zmath  isi  scopus
  • Дискретная математика
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