一类循环系的平坦性

Flatness of Some Cyclic Acts

中文关键词:  循环系  右同余  平坦性

英文关键词:cyclic act  right congruence  flatness.

中文摘要:

      设Ｓ是幺半群，ｘ_１，ｘ₂，…∈Ｓ且满足ｘ_i+１ｘ_i＝ｘ_i，ｉ＝１，２……ｙ是S中的任意元素，记H={(yx_i,x_i)|i=1,2,…}.设ρ(H)是S的由Ｈ生成的最小右同余，本文证明了S／ρ（Ｈ）是平坦右Ｓ－系．

英文摘要:

      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.