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
-
摘要: 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.Abstract: Let T_n be the full transformation semigroup on the finite set X=1,2,…,n,S_n be the subsemigroup of all singular transformations in T_n.Denote S~-_n=f∈S_n:x∈X,f(x)≤x,and O_n=f∈T_n:x,y∈X,x≤y implies(f(x)≤f(y).)Then both S~-_n and O_n are subsemigroups of T_n.Let H_n=S~-_n∩O_n.Some properties for H_n,such as,(Green's) relations,Green's starred relations,rank and idempotent rank,are observed.Among other things,it is shown that H_n is idempotent-generated and that it is generated by n-1 idempotents in J...
下载: