Test elements and the Retract Theorem for monounary algebras
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 , where each is unary and .