It is obtained that the commutative completely idempotent algebra which has unit element and no zero factor is a extension field on F. The structure of two dimension completely idempotent algebra is given out. 本文首先得出哉F上有单位元无零因子交换完全幂等代数A是F的扩域的结论,给出域F上二维完全幂等代数的结构;