半群W(n,k)的正则性与Green’s关系

Regularity and Green′s Relations of the Semigroup W(n,k)

设Xn={1,2,…,n}(n≥3),并赋予自然序,在Xn上定义一个新的变换半群:W(n,k)={f∈Tn:x,y∈Xn,|x-k|≤|y-k|■|f(x)-k|≤|f(y)-k|},k∈{2,3,…,n-1}.讨论了半群W(n,k)的正则性,并给出了其全部Green’s关系的刻画.

Let Xn = { 1,2,..., n} （n ≥3）. Let it be ordered in the standard way, and we defined a new transforma- tion semigroup in Xn. Its representation is as follows （n,k）={f∈Tn：A↓x,y∈以,｜x-k｜≤ly-k｜→f｜（＊）-kl≤｜f（y）-k｜,k∈{2,3,…,n-1} We then discussed the regularity and Green＇s relations of the semigroup W （n,k） .