Cardinality of retracts of monounary algebras

Danica Jakubíková-Studenovská; Jozef Pócs

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 2, page 469-479
  • ISSN: 0011-4642

Abstract

top
For an uncountable monounary algebra ( A , f ) with cardinality κ it is proved that ( A , f ) has exactly 2 κ retracts. The case when ( A , f ) is countable is also dealt with.

How to cite

top

Jakubíková-Studenovská, Danica, and Pócs, Jozef. "Cardinality of retracts of monounary algebras." Czechoslovak Mathematical Journal 58.2 (2008): 469-479. <http://eudml.org/doc/31222>.

@article{Jakubíková2008,
abstract = {For an uncountable monounary algebra $(A,f)$ with cardinality $\kappa $ it is proved that $(A,f)$ has exactly $2^\{\kappa \}$ retracts. The case when $(A,f)$ is countable is also dealt with.},
author = {Jakubíková-Studenovská, Danica, Pócs, Jozef},
journal = {Czechoslovak Mathematical Journal},
keywords = {monounary algebra; retract; cardinality; monounary algebra; retract; cardinality},
language = {eng},
number = {2},
pages = {469-479},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Cardinality of retracts of monounary algebras},
url = {http://eudml.org/doc/31222},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Jakubíková-Studenovská, Danica
AU - Pócs, Jozef
TI - Cardinality of retracts of monounary algebras
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 2
SP - 469
EP - 479
AB - For an uncountable monounary algebra $(A,f)$ with cardinality $\kappa $ it is proved that $(A,f)$ has exactly $2^{\kappa }$ retracts. The case when $(A,f)$ is countable is also dealt with.
LA - eng
KW - monounary algebra; retract; cardinality; monounary algebra; retract; cardinality
UR - http://eudml.org/doc/31222
ER -

References

top
  1. Functional graphs, quasiordered sets and commutative hypergroups, Publ. of Masaryk Univ., Brno (1995). (Czech) (1995) 
  2. On direct limits of finite algebras, Contributions to General Algebra 11 (Olomouc, 1998, Velké Karlovice, 1998), Heyn, Klagenfurt, (1999), 101–104. MR1696661
  3. Retract irreducibility of connected monounary algebras I, Czech. Math. J. 46 (1996), 291–308. (1996) MR1388617
  4. 10.1023/A:1022452009553, Czech. Math. J. 48 (1998), 793–808. (1998) MR1658198DOI10.1023/A:1022452009553
  5. Set Theory, Academic Press, 1978. (1978) Zbl0419.03028MR0506523
  6. Topics in Universal Algebra, Springer-Verlag, Berlin, Heidelberg, New York, 1972. (1972) MR0345895
  7. 10.1007/BF00672386, Internat. J. Theor. Phys. 26 (1987), 1–9. (1987) MR0890206DOI10.1007/BF00672386
  8. 10.1090/S0002-9939-02-06666-2, Proc. Amer. Math. Soc. 131 (2003), 1007–1010. (2003) Zbl1016.08006MR1948088DOI10.1090/S0002-9939-02-06666-2
  9. 10.1142/S0218196798000144, Int. J. Algebra Comput. 8 (1998), 295–310. (1998) MR1627824DOI10.1142/S0218196798000144
  10. Mono-unary algebras in the work of Czechoslovak mathematicians, Arch. Math. (Brno) (1990), 155–164. (1990) MR1188275
  11. Über Abbildungen von Mengen, Pacif. J. Math. 13 (1963), 1359–1369. (1963) MR0157143
  12. Unars, Colloq. Math Soc. János Bolyai, 29 Univ. Algebra, Esztergom (1977), 735-743. (1977) Zbl0376.08004MR0660907
  13. Retracts and retractions of free algebras, Russ. Math. 42 (1998), 65–77. (1998) Zbl0926.08002MR1612947
  14. 10.1007/BF01194236, Arch. Math. 60 (1993), 36–39. (1993) Zbl0806.16016MR1193091DOI10.1007/BF01194236

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.