| Title:
|
Test elements and the Retract Theorem for monounary algebras (English) |
| Author:
|
Jakubíková-Studenovská, Danica |
| Author:
|
Pócs, Jozef |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
3 |
| Year:
|
2007 |
| Pages:
|
975-986 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The term “Retract Theorem” has been applied in literature in connection with group theory. In the present paper we prove that the Retract Theorem is valid (i) for each finite structure, and (ii) for each monounary algebra. On the other hand, we show that this theorem fails to be valid, in general, for algebras of the form $\mathcal{A}=(A,F)$, where each $f\in F$ is unary and $\operatorname{card}F >1$. (English) |
| Keyword:
|
monounary algebra |
| Keyword:
|
retract |
| Keyword:
|
test element |
| MSC:
|
08A60 |
| idZBL:
|
Zbl 1174.08302 |
| idMR:
|
MR2356934 |
| . |
| Date available:
|
2009-09-24T11:51:02Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128220 |
| . |
| Reference:
|
[1] D. Jakubíková-Studenovská: Retract irreducibility of connected monounary algebras I.Czech. Math. J. 46 (1996), 291–308. MR 1388617 |
| Reference:
|
[2] B. Jónsson: Topics in universal algebra.Springer-Verlag, Berlin, Heidelberg, New York, 1972. MR 0345895 |
| Reference:
|
[3] E. Nelson: Homomorphism of mono-unary algebras.Pacif. J. Math. 99, 2 (1982), 427–429. 10.2140/pjm.1982.99.427 |
| Reference:
|
[4] J. C. O’Neill and E. C. Turner: Test elements and the Retract Theorem in Hyperbolic groups.New York J. of Math. 6 (2000), 107–117. MR 1772562 |
| Reference:
|
[5] J. Nielsen: Die Automorphismen der allgemeiner unendlichen Gruppe mit zwei Erzeugenden.Math. Ann. 78 (1918), 385–397. |
| Reference:
|
[6] M. Novotný: Über Abbildungen von Mengen.Pacif. J. Math. 13 (1963), 1359–1369. MR 0157143 |
| Reference:
|
[7] M. Novotný: Mono-unary algebras in the work of Czechoslovak mathematicians.Arch. Math. (Brno) 26 (1990), 155–164. MR 1188275 |
| Reference:
|
[8] E. C. Turner: Test words for automorphisms of free groups.Bull. London Math. Soc. 28 (1996), 255–263. Zbl 0852.20022, MR 1374403, 10.1112/blms/28.3.255 |
| Reference:
|
[9] D. A. Voce: Test words and stable image of an endomorphism.PhD Thesis, Univ. at Albany, 1995. |
| . |
