Algebra universalis

, 79:10 | Cite as

The lattice of convexities of partial monounary algebras

  • Miroslava Černegová
  • Danica Jakubíková-Studenovská
Article
  • 4 Downloads
Part of the following topical collections:
  1. In memory of Bjarni Jónsson

Abstract

A class of partial monounary algebras is called a convexity if it is closed under homomorphic images, direct products and convex relative subalgebras. We prove that the collection of all convexities of partial monounary algebras forms a countable set. Further, each convexity can be generated by at most two algebras.

Keywords

Partial monounary algebra Convex relative subalgebra Convexity 

Mathematics Subject Classification

08A60 

References

  1. 1.
    Burmeister, P.: A Model Theoretic Oriented Approach to Partial Algebras. Introduction to Theory and Application of Partial Algebras. Part I, Mathematical Research, vol. 32. Akademie-Verlag, Berlin (1986)Google Scholar
  2. 2.
    Mlitz, R. (ed.): General algebra. In: Proc. Internat. Conf. Krems 1988, North Holland, Amsterdam (1990)Google Scholar
  3. 3.
    Grätzer, G.: Universal Algebra, 2nd edn. Springer, New York (1979)MATHGoogle Scholar
  4. 4.
    Jakubík, J.: On convexities of lattices. Czechoslov. Math. J. 42(117), 325–330 (1992)MathSciNetMATHGoogle Scholar
  5. 5.
    Jakubíková-Studenovská, D.: Convex subsets of partial monounary algebras. Czechoslov. Math. J. 38(113), 655–672 (1988)MathSciNetMATHGoogle Scholar
  6. 6.
    Jakubíková-Studenovská, D.: On the lattice of convex subsets of a partial monounary algebra. Czechoslov. Math. J. 39(114), 502–522 (1989)MathSciNetMATHGoogle Scholar
  7. 7.
    Jakubíková-Studenovská, D.: On directed convex subsets of partial monounary algebras. Czechoslov. Math. J. 43(118), 675–694 (1993)MathSciNetMATHGoogle Scholar
  8. 8.
    Jakubíková-Studenovská, D.: Convex automorphisms of partial monounary algebras. Czechoslov. Math. J. 45(120), 393–412 (1995)MathSciNetMATHGoogle Scholar
  9. 9.
    Jakubíková-Studenovská, D.: Convexities of partial monounary algebras. Algebra Universalis 60, 125–143 (2009)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Jakubíková-Studenovská, D., Pócs, J.: Monounary Algebras. P.J. Šafárik University, Košice (2009)MATHGoogle Scholar
  11. 11.
    Jónsson, B.: Topics in Universal Algebra. Lecture Notes in Mathematics, vol. 250. Springer, Berlin (1972)Google Scholar
  12. 12.
    Pitkethly, J.G., Davey, B.A.: Dualisability: Unary Algebras and Beyond. Springer, New York (2005)MATHGoogle Scholar
  13. 13.
    Pócs, J.: A note on the convexity of lattices generated by the set of nonnegative integers. Mathematica Slovaca 64, 555–562 (2014)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Miroslava Černegová
    • 1
  • Danica Jakubíková-Studenovská
    • 1
  1. 1.Institute of Mathematics, Faculty of SciencePavol Jozef Šafárik University in KošiceKosiceSlovakia

Personalised recommendations