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.