Subdirect products of certain varieties of unary algebras
J. Płonka in [12] noted that one could expect that the regularization of a variety of unary algebras is a subdirect product of and the variety of all discrete algebras (unary semilattices), but is not the case. The purpose of this note is to show that his expectation is fulfilled for those and only those irregular varieties which are contained in the generalized variety of the so-called trap-directable algebras.