π-逆半群剩余的有限性

On residual finiteness of π-inverse semigroup

剩余有限性是半群中比较重要的有限性条件之一 ,它和算法问题紧密相关 .研究了π -逆半群的剩余有限性 ,证明了 :若一个π -逆半群是剩余有限的 ,则每个主因子要么是零积半群 ,要么是带零群 ,要么是 Brandt半群 ;刻画了π -逆半群的主因子的剩余有限性 ;同时得到了π -逆半群是剩余有限的一个充分条件 .

Residual finiteness is one of the more important finiteness conditions.It has tight correlation with algorithmic problem.The residual finiteness of π-inverse semigroups was studied in this paper.It was proved that if a π-inverse semigroup S is residual finite,then every principal factor of S is either null or group with 0 or Brandt semigroup.It was also characterized that the residual finiteness of principal factors of a π-inverse semigroup.At the same time,a sufficient condition that a π-inverse semigroup is residual finite was got.