Test elements and the Retract Theorem for monounary algebras
Danica Jakubíková-Studenovská; Jozef Pócs
Czechoslovak Mathematical Journal (2007)
- Volume: 57, Issue: 3, page 975-986
- ISSN: 0011-4642
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topJakubíková-Studenovská, Danica, and Pócs, Jozef. "Test elements and the Retract Theorem for monounary algebras." Czechoslovak Mathematical Journal 57.3 (2007): 975-986. <http://eudml.org/doc/31176>.
@article{Jakubíková2007,
abstract = {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 $\operatorname\{card\}F >1$.},
author = {Jakubíková-Studenovská, Danica, Pócs, Jozef},
journal = {Czechoslovak Mathematical Journal},
keywords = {monounary algebra; retract; test element; monounary algebra; retract; test element},
language = {eng},
number = {3},
pages = {975-986},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Test elements and the Retract Theorem for monounary algebras},
url = {http://eudml.org/doc/31176},
volume = {57},
year = {2007},
}
TY - JOUR
AU - Jakubíková-Studenovská, Danica
AU - Pócs, Jozef
TI - Test elements and the Retract Theorem for monounary algebras
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 3
SP - 975
EP - 986
AB - 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 $\operatorname{card}F >1$.
LA - eng
KW - monounary algebra; retract; test element; monounary algebra; retract; test element
UR - http://eudml.org/doc/31176
ER -
References
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