Gomes described the r - unipotent congruence on a regular semigroup s by means of its kernal and hyper - trace . in this paper , we describe the r - semiprime r - unipotent congruence and the r - semiprime e - left normal congruence on a strong - regular semigroup Gomes利用同余的核与超迹描述了正则半群上的r -幂同余，但在更广义的半群上还没有这方面的讨论。
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In the first part . firstly we introduce a new class of semigroup s called r - unipotent e - inversive seniigroup . serondly we describe the strong congruences on s in terms of their kernels and traces . ve prove that a strong congruence on s can present a strong congruence pair : conversely . a strong congruence pair on s can determine a strong congruence 接着用“核-迹”方法研究s上的强同余，即证明s上的任一强同余，可以决定s的一个强同余对，反之s的任一强同余对，可以决定s上的一个强同余。
