Let S be a monoid,and y,x1,x2,… be in S such that xi+1xi=xi,(i=1,2…). Denote by ρ(H ) the right congruence generated by H={(yxi,xi)|i=1,2,…}. We proved that the right S -act S/ρ(H ) is flat. As a corollary, the result of [4] follows directly, which says that,if x is a regular element of S, then S/ρ(yx,x ) is flat. |