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A network of congruences on an ample semigroup
Semigroup Forum ( IF 0.7 ) Pub Date : 2021-03-16 , DOI: 10.1007/s00233-021-10168-z
Abdulsalam El-Qallali

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.



中文翻译:

充分半群上的同余网络

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。

更新日期:2021-03-16
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