π-逆半群剩余的有限性  

On residual finiteness of π-inverse semigroup

作　　者：田振际[1] 严克明[1] 李敦刚[1] 

机构地区：[1]甘肃工业大学理学院,甘肃兰州730050

出　　处：《兰州大学学报（自然科学版）》2003年第3期4-7,共4页Journal of Lanzhou University(Natural Sciences)

基　　金：甘肃工业大学优秀青年教师计划基金资助项目 ( 2 0 0 2 92 0 ) .

摘　　要：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.

关 键 词：π—逆半群 剩余有限性 主因子 BRANDT半群 

分 类 号：O172.7[理学—数学]