For n E N,let On be the semigroup of all singular order-preserving mappings on[n]=(1,2,...,n}.For each nonempty subset A of[n],let On(A)=(a∈On:(A k∈A)ka≤k}be the semigroup of all order-preserving and A-decreasing m...For n E N,let On be the semigroup of all singular order-preserving mappings on[n]=(1,2,...,n}.For each nonempty subset A of[n],let On(A)=(a∈On:(A k∈A)ka≤k}be the semigroup of all order-preserving and A-decreasing mappings on[n].In this paper it is shown that On(A)is an abundant semigroup with n-1*-classes.Moreover,On(A)is idempotent-generated and its idempotent rank is 2n-2-IA/(n}l.Further,it is shown that the rank of On(A)is equal to n-1 if 1∈A,and it is equal to n otherwise.展开更多
基金supported by the Natural Science Fund of Guizhou(No.【2010】3174)
文摘For n E N,let On be the semigroup of all singular order-preserving mappings on[n]=(1,2,...,n}.For each nonempty subset A of[n],let On(A)=(a∈On:(A k∈A)ka≤k}be the semigroup of all order-preserving and A-decreasing mappings on[n].In this paper it is shown that On(A)is an abundant semigroup with n-1*-classes.Moreover,On(A)is idempotent-generated and its idempotent rank is 2n-2-IA/(n}l.Further,it is shown that the rank of On(A)is equal to n-1 if 1∈A,and it is equal to n otherwise.
