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Test elements and the Retract Theorem for monounary algebras
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 975-986 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $\operatorname{card}F >1$.
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 $\operatorname{card}F >1$.
Classification : 08A60
Keywords: monounary algebra; retract; test element 
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     author = {Jakub{\'\i}kov\'a-Studenovsk\'a, Danica and P\'ocs, Jozef},
     title = {Test elements and the {Retract} {Theorem} for monounary algebras},
     journal = {Czechoslovak Mathematical Journal},
     pages = {975--986},
     year = {2007},
     volume = {57},
     number = {3},
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     zbl = {1174.08302},
     language = {en},
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}
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Jakubíková-Studenovská, Danica; Pócs, Jozef. Test elements and the Retract Theorem for monounary algebras. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 975-986. http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a14/