(LO)BG的两种分解

Two Solutions of(LO)BG

令S∈(LO)BG,在S上定义二元关系:xRy当且仅当存在a,b∈S,使得x,y∈aSb且x=x0yx0,y=y0xy0.证明了η=Rt是S上的一个幂等元纯的正规密码群并半群同余.在此基础上,利用格林关系和同余的方法证明了(LO)BG=NBG∨B及(LO)BG=NBG∨(LO)

Let S∈（LO）BG ,and the binary relation is defined on S as：xRy if and only if （ a ,b ∈ S）x ,y ∈aSb , x = x0 yx0 ,y= y0 xy0 .It is proved thatη= Rt is an idempotent pure congruence on S .Based on that , coupled with Green＇s relation and the method of congruences ,we prove that.