T(ρ,≤)的Green关系和正则元

Green Relations and Regular Elements of Partition Order-decreasing Transformation Monoids

设Tn是Xn={1,2,…,n}上的全变换半群.设ρ是Xn上的一个等价关系,≤是Xn/ρ上的一个全序.对Xn上Tn的划分递减子幺半群T(ρ,≤)={α∈Tn:(xα)ρ≤xρ,x∈Xn},文中刻划出它的Green关系和正则元.

Let Tn be the full transformation semigroup on a finite set Xn= {1 ,2 ,…… ,n}.Let ρbe an equivalence relation on Xn ,and let ≤ be a total order on the partition set Xn/ρ.Consider partition decreasing submonoids as T（ρ,≤ ）= {α∈Tn ：（xα）ρ≤ xρ,？ x ∈ Xn}.The Green relations and regular elements of T（ρ,≤ ） are descibed .