对称逆半群的中心化子为Clifford半群时的自同构与内自同构

设C。为有限集Xn={1，2，…，n}上的对称逆半群，令ξ∈Cn 且}为ξ元，C（ξ）为Clifford半群．文章通过Clifford半群以及半群自同构的定义得到此种情况下ξ的中心化子C（ξ）={α∈C。｜αξ=ξα}自同构的充要条件，及此时自同构为内自同构的充要条件即厂为C（ξ）到C（ξ）的内自同构则f为恒等映射．

Automorphisms and Inner Automorphisms of Centralizers of Group Element to Be A Clifford Semigroup on the Finite Symmetric Inverse Semigroup

Let Cn be the symmetric inverse semigroup on the finite set Xn= { 1,2,..., n}, and ξ is a group elements of Cn, C（ξ） is a Clifford semigroup. The paper researches on the definition of Clifford semigroup and automorphisms obtains a sufficient and necessary condition for the automorphisms of C（ξ）= {α∈Cn｜ 6ξα=ξα}. And a sufficient and necessary condition for the automorphisms is an inner automorphism, that is if f is an inner automorphism from C（ξ） to C（ξ）, then f must be a identity mapping.