On 2-homogeneity of monounary algebras

Danica Jakubíková-Studenovská

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 1, page 55-68
  • ISSN: 0011-4642

Abstract

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Fraïssé introduced the notion of a k -set-homogeneous relational structure. In the present paper the following classes of monounary algebras are described: 𝒮 h 2 ( S ) , 𝒮 h 2 ( S c ) , 𝒮 h 2 ( P c ) —the class of all algebras which are 2-set-homogeneous with respect to subalgebras, connected subalgebras, connected partial subalgebras, respectively, and ℋ 2 ( S ) , ℋ 2 ( S c ) , ℋ 2 ( P c ) —the class of all algebras which are 2-homogeneous with respect to subalgebras, connected subalgebras, connected partial subalgebras, respectively.

How to cite

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Jakubíková-Studenovská, Danica. "On 2-homogeneity of monounary algebras." Czechoslovak Mathematical Journal 53.1 (2003): 55-68. <http://eudml.org/doc/30758>.

@article{Jakubíková2003,
abstract = {Fraïssé introduced the notion of a $k$-set-homogeneous relational structure. In the present paper the following classes of monounary algebras are described: $\mathcal \{S\}h_2(S)$, $\mathcal \{S\}h_2(S^c)$, $\mathcal \{S\}h_2(P^c)$ —the class of all algebras which are 2-set-homogeneous with respect to subalgebras, connected subalgebras, connected partial subalgebras, respectively, and $\mathcal \{H\}_2(S)$, $\mathcal \{H\}_2(S^c)$, $\mathcal \{H\}_2(P^c)$ —the class of all algebras which are 2-homogeneous with respect to subalgebras, connected subalgebras, connected partial subalgebras, respectively.},
author = {Jakubíková-Studenovská, Danica},
journal = {Czechoslovak Mathematical Journal},
keywords = {monounary algebra; homogeneous; 2-homogeneous; 2-set-homogeneous; monounary algebra; 2-homogeneous; 2-set-homogeneous},
language = {eng},
number = {1},
pages = {55-68},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On 2-homogeneity of monounary algebras},
url = {http://eudml.org/doc/30758},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Jakubíková-Studenovská, Danica
TI - On 2-homogeneity of monounary algebras
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 1
SP - 55
EP - 68
AB - Fraïssé introduced the notion of a $k$-set-homogeneous relational structure. In the present paper the following classes of monounary algebras are described: $\mathcal {S}h_2(S)$, $\mathcal {S}h_2(S^c)$, $\mathcal {S}h_2(P^c)$ —the class of all algebras which are 2-set-homogeneous with respect to subalgebras, connected subalgebras, connected partial subalgebras, respectively, and $\mathcal {H}_2(S)$, $\mathcal {H}_2(S^c)$, $\mathcal {H}_2(P^c)$ —the class of all algebras which are 2-homogeneous with respect to subalgebras, connected subalgebras, connected partial subalgebras, respectively.
LA - eng
KW - monounary algebra; homogeneous; 2-homogeneous; 2-set-homogeneous; monounary algebra; 2-homogeneous; 2-set-homogeneous
UR - http://eudml.org/doc/30758
ER -

References

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  10. On homogeneous and 1-homogeneous monounary algebras, In: Contributions to General Algebra 12.  Proceedings of the Vienna Conference, June, 1999, Verlag J. Heyn, Klagenfurt, 2000, pp. 222–224. (2000) 
  11. 10.4064/fm-56-1-81-103, Fund. Math. 56 (1964), 81–103. (1964) MR0176950DOI10.4064/fm-56-1-81-103
  12. Homogeneous partially ordered sets, In: Finite and Infinite Combinatorics in Sets and Logic. Proceeding NATO ASI conference in Banf 1991, N. W.  Sauer, R. E.  Woodrow and B.  Sands (eds.), Kluwer, Dordrecht, 1993, pp. 279–288. (1993) Zbl0845.06002MR1261211
  13. Some questions about complete Boolean algebras, In: Lattice Theory, Proc. Symp. Pure Math, Vol.  II, AMS, Providence, 1961, pp. 129–140. (1961) Zbl0101.27104MR0138570

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