Flatness of Some Cyclic Acts

Abstract:

      Let S be a monoid,and y,ｘ_１，ｘ₂，… be in S such that ｘ_i+１ｘ_i＝ｘ_i，(ｉ＝１，２…). Denote by ρ(H ) the right congruence generated by H={(yx_i,x_i)|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.