A Correction on the Paper 'Characterization of Monoids by Properties of Generators'

A theorem in the article “Characterization of Monoids by Properties of Generators,” written by Kilp and Knauer, states that amalgamated coproducts of generators are generators in the category Act -S of right S-acts over a monoid S. In this note we give a counterexample to deny this theorem. However, we show that the results in that article based on the mentioned theorem still remain valid. Moreover, an incorrect proposition in the monograph Monoids, Acts and Categories by Kilp et al. which states that coamalgamated product of cogenerators are cogenerators is denied by a counterexample.