It is obtained that the integer completely idempotent rings are fields . two characterization are gained that the completely idempotent rings with element are l - semisimple and b - semisimple . a class of finite completely idempotent rings is solved with | r | - p2 首先得出整完全幂等环是域的结论，其次给出有单位元的完全幂等环的两个刻划，即有单位的完全幂等环是l -半单的， b -半单的，最后给出了一类有限完全幂等环的结构
