Geodesic
On 2-homogeneity of monounary algebras
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 1, pp. 55-68 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Fraïssé introduced the notion of a $k$-set-homogeneous relational structure. In the present paper the following classes of monounary algebras are described: $\mathcal Sh_2(S)$, $\mathcal Sh_2(S^c)$, $\mathcal Sh_2(P^c)$ —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.
Fraïssé introduced the notion of a $k$-set-homogeneous relational structure. In the present paper the following classes of monounary algebras are described: $\mathcal Sh_2(S)$, $\mathcal Sh_2(S^c)$, $\mathcal Sh_2(P^c)$ —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.
Classification : 08A60
Keywords: monounary algebra; homogeneous; 2-homogeneous; 2-set-homogeneous 
@article{CMJ_2003_53_1_a4,
     author = {Jakub{\'\i}kov\'a-Studenovsk\'a, Danica},
     title = {On 2-homogeneity of monounary algebras},
     journal = {Czechoslovak Mathematical Journal},
     pages = {55--68},
     year = {2003},
     volume = {53},
     number = {1},
     mrnumber = {1961998},
     zbl = {1014.08005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2003_53_1_a4/}
}
TY  - JOUR
AU  - Jakubíková-Studenovská, Danica
TI  - On 2-homogeneity of monounary algebras
JO  - Czechoslovak Mathematical Journal
PY  - 2003
SP  - 55
EP  - 68
VL  - 53
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMJ_2003_53_1_a4/
LA  - en
ID  - CMJ_2003_53_1_a4
ER  - 
%0 Journal Article
%A Jakubíková-Studenovská, Danica
%T On 2-homogeneity of monounary algebras
%J Czechoslovak Mathematical Journal
%D 2003
%P 55-68
%V 53
%N 1
%U http://geodesic.mathdoc.fr/item/CMJ_2003_53_1_a4/
%G en
%F CMJ_2003_53_1_a4
Jakubíková-Studenovská, Danica. On 2-homogeneity of monounary algebras. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 1, pp. 55-68. http://geodesic.mathdoc.fr/item/CMJ_2003_53_1_a4/

[1] B.  Csákány: Homogeneous algebras. In: Contributions to General Algebra. Proc. Klagenfurt Conference, 1978, Verlag J.  Heyn, Klagenfurt, 1979, pp. 77–81. | MR

[2] B.  Csákány: Homogeneous algebras are functionally complete. Algebra Universalis 11 (1980), 149–158. | DOI | MR

[3] B.  Csákány and T. Gavalcová: Finite homogeneous algebras  I. Acta Sci. Math. 42 (1980), 57–65. | MR

[4] M.  Droste and H. D.  Macpherson: On $k$-homogeneous posets and graphs. J.  Comb. Theory Ser. A 56 (1991), 1–15. | DOI | MR

[5] M.  Droste, M.  Giraudet, H. D.  Macpherson and N.  Sauer: Set-homogeneous graphs. J.  Comb. Theory Ser. B 62 (1994), 63–95. | DOI | MR

[6] M.  Droste, M.  Giraudet and D.  Macpherson: Set-homogeneous graphs and embeddings of total orders. Order 14 (1997), 9–20. | DOI | MR

[7] R.  Fraïssé: Theory of Relations. North-Holland, Amsterdam, 1986. | MR

[8] B.  Ganter, J.  Płonka and H.  Werner: Homogeneous algebras are simple. Fund. Math. 79 (1973), 217–220. | DOI | MR

[9] D.  Jakubíková-Studenovská: Homogeneous monounary algebras. Czechoslovak Math.  J. 52 (2002), 309–317. | DOI | MR

[10] D.  Jakubíková-Studenovská: 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.

[11] E.  Marczewski: Homogeneous algebras and homogeneous operations. Fund. Math. 56 (1964), 81–103. | DOI | MR

[12] A. H.  Mekler: 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. | MR | Zbl

[13] R. S.  Pierce: Some questions about complete Boolean algebras. In: Lattice Theory, Proc. Symp. Pure Math, Vol.  II, AMS, Providence, 1961, pp. 129–140. | MR | Zbl