For an admissible congruence \(\gamma \) on an ample semigroup S, the minimum admissible congruence \(\gamma _t\) whose trace is \(\mathrm {tr}\gamma \) has been determined by the author, and Fountain, Gomes and Gould. With some restriction on \(\gamma \), we characterize in this paper the minimum admissible congruence \((\gamma _t)_k\) whose kernel is \(\mathrm {ker}\gamma _t\), as well as the minimum admissible congruence \(((\gamma _t)_k)_t\) whose trace is \(\mathrm {tr}(\gamma _t)_k\). These results extend the corresponding results of Petrich and Reilly in the inverse semigroup case. Meanwhile, some particular minimum admissible congruences on S are recognized and this information is applied to set up a network of certain minimum admissible congruences on S.

对于可容许同余\（\伽马\）上的充足半群小号，最小允许同余\（\伽马_t \） ，其轨迹是\（\ mathrm {TR} \伽马\）已经由作者确定，并且喷泉，戈麦斯和古尔德。在对\（\ gamma \）有一些限制的情况下，我们在本文中描述了最小可容许同余\（（（gamma _t）_k \），其核是\（\ mathrm {ker} \ gamma _t \）以及迹线为\（\ mathrm {tr}（\ gamma _t）_k \）的最小容许同余\（（（（\ gamma _t）_k）_t \）。这些结果扩展了反半群情况下Petrich和Reilly的相应结果。同时，识别出关于S的一些特定的最小容许同余，并且将该信息应用于建立关于S的某些最小容许同余的网络。