Title:
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On 2-homogeneity of monounary algebras (English) |
Author:
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Jakubíková-Studenovská, Danica |
Language:
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English |
Journal:
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Czechoslovak Mathematical Journal |
ISSN:
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0011-4642 (print) |
ISSN:
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1572-9141 (online) |
Volume:
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53 |
Issue:
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1 |
Year:
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2003 |
Pages:
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55-68 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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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: $\mathcal Sh_2(S)$, $\mathcal Sh_2(S^c)$, $\mathcal Sh_2(P^c)$ —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. (English) |
Keyword:
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monounary algebra |
Keyword:
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homogeneous |
Keyword:
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2-homogeneous |
Keyword:
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2-set-homogeneous |
MSC:
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08A60 |
idZBL:
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Zbl 1014.08005 |
idMR:
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MR1961998 |
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Date available:
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2009-09-24T10:58:58Z |
Last updated:
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2020-07-03 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/127780 |
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Reference:
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[1] B. Csákány: Homogeneous algebras.In: Contributions to General Algebra. Proc. Klagenfurt Conference, 1978, Verlag J. Heyn, Klagenfurt, 1979, pp. 77–81. MR 0537408 |
Reference:
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[2] B. Csákány: Homogeneous algebras are functionally complete.Algebra Universalis 11 (1980), 149–158. MR 0588208, 10.1007/BF02483093 |
Reference:
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[3] B. Csákány and T. Gavalcová: Finite homogeneous algebras I.Acta Sci. Math. 42 (1980), 57–65. MR 0576935 |
Reference:
|
[4] M. Droste and H. D. Macpherson: On $k$-homogeneous posets and graphs.J. Comb. Theory Ser. A 56 (1991), 1–15. MR 1082839, 10.1016/0097-3165(91)90018-C |
Reference:
|
[5] M. Droste, M. Giraudet, H. D. Macpherson and N. Sauer: Set-homogeneous graphs.J. Comb. Theory Ser. B 62 (1994), 63–95. MR 1290631, 10.1006/jctb.1994.1055 |
Reference:
|
[6] M. Droste, M. Giraudet and D. Macpherson: Set-homogeneous graphs and embeddings of total orders.Order 14 (1997), 9–20. MR 1468952, 10.1023/A:1005880810385 |
Reference:
|
[7] R. Fraïssé: Theory of Relations.North-Holland, Amsterdam, 1986. MR 0832435 |
Reference:
|
[8] B. Ganter, J. Płonka and H. Werner: Homogeneous algebras are simple.Fund. Math. 79 (1973), 217–220. MR 0319859, 10.4064/fm-79-3-217-220 |
Reference:
|
[9] D. Jakubíková-Studenovská: Homogeneous monounary algebras.Czechoslovak Math. J. 52 (2002), 309–317. MR 1905437, 10.1023/A:1021722527256 |
Reference:
|
[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. |
Reference:
|
[11] E. Marczewski: Homogeneous algebras and homogeneous operations.Fund. Math. 56 (1964), 81–103. MR 0176950, 10.4064/fm-56-1-81-103 |
Reference:
|
[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. Zbl 0845.06002, MR 1261211 |
Reference:
|
[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. Zbl 0101.27104, MR 0138570 |
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