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中文摘要：
证明了完全0-单半群的真同态像仍完全0-单，给出了其结构；刻画了完全0-单半群的最大真同余及其商；给出了有0和本原幂等元的半群S无同余的充要条件；讨论了完全0-单半群上的幂等元纯同余，幂等元分离同余及其同态像；给出了完全0-单半群存在0-群同余的充要条件并刻画了其0-群同态像．
英文摘要：
In this paper, it is proved that proper homomorphic images of a completely 0-simple semigroup are also completely 0- simple. The structure of the images is described. The maximum proper congruence on a completely 0-simple semigroup and its image are characterized. The sufficient and necessary condition for a semigroup with 0 and primitive idempotent to be congruence-free is given. Idempotet-pure and idempotent-separating congruences on a completely 0-simple semigroup and their images are discussed. The sufficient and necessary condition for a completely 0-simple semigroup to have 0-group congruence is given and the 0-group homomorphic images are characterized.
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