单调保k变换半群OR_n(K)的Green关系

Green’s Relations of Semigroup Monotone and k-Preserving Transformations

设Xn=﹛1,2,...n﹜是有限集, Singn是Xn上的奇异变换半群,On和Rn是Singn上的保序变换之集和反保序变换之集,令ORn(K) =﹛α∈On:Kα=K﹜∪﹛α∈Rn:Kα=K﹜,刻画了半群ORn(K)的Green关系。

Let Xn=﹛1,2,...n﹜denote a finite set, Singn is Singular transformation semigroups on it. On and Rn is Order-preserving and anti-order-preserving transformation semigroups of Singn.Let ORn(K)=﹛α∈On:Kα=K﹜∪﹛α∈Rn:Kα=K﹜,this paper describes Green’s relations of ORn(K).