Subdirect products of certain varieties of unary algebras

J. Plonka in [12] noted that one could expect that the regularization ℛ(K) of a variety K of unary algebras is a subdirect product of K and the variety D 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 K which are contained in the generalized variety TDir of the so-called trap-directable algebras.