A note on orthodox semidirect products and wreath products of monoids

In the present note, we show that the restriction which Saito imposed on S in [3] is not necessary: S may be a semigroup without unity. Secondly we investigate the wreath products of semigroups and obtain our main results, Theorem 2.3 and Corollary 2.4. We find also that groups in [3] may be replaced by right groups in [1]. Undefined terminology and notation may be found in [3] and [1] unless otherwise stated.