On flatness of acts

We consider monoids $S=G\dot \cup I$ where G is a group and I is an ideal of S and show that if an S-act is principally weakly flat, (weakly) flat, torsion free or satisfies conditions (P) or (P_E) as an I¹-act, then it has these properties as an S-act. We also show that an S-act which is free, projective or strongly flat as an I¹-act may not generally have these properties as an S-act.