Regularity and Green′s Relations of the Semigroup W(n,k)
Wen Teng · Journal of Jiaying University · 2013
Let Xn={1,2,…,n}(n ≥3).Let it be ordered in the standard way,and we defined a new transformation semigroup in Xn.Its representation is as follows :W(n,k)={f∈Tn:x,y∈Xn,|x-k|≤|y-k|■|f(x)-k|≤|f(y)-k|},k∈{2,3,…,n-1}.We then discussed the regularity and Green′s relations of the semigroup W(n,k).