Test elements and the retract theorem for monounary algebras

Author: Jakubíková-Studenovská Danica  

Publisher: Springer Publishing Company

ISSN: 0011-4642

Source: Czechoslovak Mathematical Journal, Vol.57, Iss.3, 2007-09, pp. : 975-986

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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 A=(A, F), where each fF is unary and card F > 1.