In the category of left S-acts, S a monoid, M is called flat if the functor $\otimes M$ preserves monomorphisms and strongly flat if it preserves equalizers and pullbacks. Theorem. If in S any two principal right ideals intersect, then all flat cyclic left S-acts are strongly flat iff $\vert S\vert =1$ or $S=T\sp 1$ where T is a nil semigroup.
U.Knauer