Lobachevskii Journal of Mathematics

, Volume 39, Issue 1, pp 138–141 | Cite as

On Categorical Equivalence Between Formations of Monounary Algebras

  • A. L. Rasstrigin


A formation is a class of algebras that is closed under homomorphic images and finite subdirect products. Every formation can be considered as a category. We prove that two formations of monounary algebras with finitely many cycles are equivalent as categories if and only if they coincide.

Keywords and phrases

Formation monounary algebra unar category category equivalence endomorphism 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    W. Gaschütz, “Zur theorie der endlichen auflösbaren Gruppen,” Math. Zeitschr. 80, 300–305 (1963).CrossRefMATHGoogle Scholar
  2. 2.
    L. A. Shemetkov, Formations of Finite Groups (Nauka, Moscow, 1978) [in Russian].MATHGoogle Scholar
  3. 3.
    L. A. Shemetkov and A. N. Skiba, Formations of Algebraic Systems (Nauka, Moscow, 1989) [in Russian].MATHGoogle Scholar
  4. 4.
    A. L. Rasstrigin, “Formations of finite monounary algebras,” Chebyshev. Sb. 12 (2), 102–109 (2011).MathSciNetMATHGoogle Scholar
  5. 5.
    D. Jakubíková-Studenovskáand J. Pócs, “Formations of finite monounary algebras,” Algebra Univ. 68, 249–255 (2012).MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    G. H. Wenzel, “Subdirect irreducibility and equational compactness in unary algebras 〈A; f〉,” Arch. Math. 21, 256–264 (1970).MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    A. L. Rasstrigin, “On heredity of formations of monounary algebras,” Izv. Saratov. Univ., Mat.Mekh. Inform. 13 (4), 108–113 (2013).MATHGoogle Scholar
  8. 8.
    A. L. Rasstrigin, “On lattices of formations of monounary algebras with finitely many cycles,” Lobachevskii J. Math. 36, 419–425 (2015).MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    V. K. Kartashov, “Quasivarieties of unars,” Math. Notes 27, 5–12 (1980).MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    B. V. Popov, “Semigroups of endomorphisms of some unary algebras,” Vestn. Vostochnoukr. Gos. Univ. 5 (27), 19–23 (2000).Google Scholar
  11. 11.
    M. S. Tsalenko and E. G. Shulgeifer, Fundamentals of Category Theory (Nauka, Moscow, 1974) [in Russian].Google Scholar
  12. 12.
    E. Nelson, “Homomorphisms of mono-unary algebras,” Pacif. J. Math. 99, 427–429 (1982).CrossRefMATHGoogle Scholar
  13. 13.
    D. Jakubíková-Studenovskáand J. Pócs, Monounary Algebras (Pavol Jozef Šafárik Univ. UPJŠ, Košice, 2009).MATHGoogle Scholar
  14. 14.
    S. V. Sirovatskaya, “On endomorphism semigroup of connected monounary algebras with one-element cycle,” Chebyshev. Sb. 14 (4), 188–195 (2013).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Volgograd State Socio-Pedagogical UniversityVolgogradRussia

Personalised recommendations