降序且保序的有限全变换半群(英文)

On the Semigroup of Order-decreasing and Order-preserving Finite Full Transformations

设Jn为有限集X={1,2,…,n}上的全变换半群,Sn为Jn中所有奇异变换构成的子半群,记Sn-={f∈Sn:x∈X,f(x)≤x},Qn={f∈Jn:x,y∈X,x≤y f(x)≤f(y)},那么Sn-与Qn都是Tn的子半群,令Hn=S-n∩Qn,则Hn也是Jn的一个子半群,Hn的某些性质,诸如Green关系,Green星关系,秩和幂等秩都进行了研究,还证明了Hn是幂等元生成的,且可由J*中的n-1个幂等元生成.

Let Tn be the full transformation semigroup on the finite set X = { 1,2,…,n} ,Sn be the subsemigroup of all singular transformations in Tn. Denote Sn = {f∈Sn ：A↓∈Xnf（x） ≤x } , and On = {f∈Tn ： A↓x, y ∈ X, x ≤ y implies f（x） ≤f（y） }. Then both S^- and On are subsemigroups of Tn. Let Hn = Sn- ∩ On. Some properties for Hn, such as, Green＇s relations,Green＇s starred relations,rank and idempotent rank,are observed. Among other things,it is shown that Hn is idempotent-generated and that it is generated by n - 1 idempotents in Jn-1.