On V. Fleischer's characterization of absolutely flat monoids

Monoids over which all weakly flat acts are flat

“…In [8] V. Fleischer proved that, for any monoid S, if all left and right S-sets are weakly flat, then in fact they are all flat. Our paper [5] gives an alternative proof of this result. Using similar ideas we obtain the following:…”

“…(In (2) we define b { =b and b n + i =b'.) By (R 1 ) there exist q h r,eS (1 g i^n -1) such that (5) for ie {1,..., n -1}. We now proceed by induction on n.…”

“…S containing (u i+1 ,v t ), we obtain 1 = a 1 + 1 s 1 + 1 (5) for ie {1,..., n -1}. We now proceed by induction on n.…”