纯正半群上的同余扩张(一)

Congruence Extensions on Regular Semigroups (1)

刻划半群上的同余及其扩张是半群的代数理论中的一个非常重要的课题．本文讨论了带上的同余的正规性和不变性以及在其Ｈａｌｌ半群上的扩张，从同余扩张的角度刻划了带上的同余的性质，给出了扩张的极大、极小同余的描述．

It is very importent to study congruences and congruence extensions on semigroups. Many authors, such as Petrich, Pastijn, Jones, Trotter and Stralka etc.,put their most interests into this field. Some kinds of congruences on semigroups had been investigated by means of congruence pairs, see, for example, [1],[5],[6] and [7]. In particular, the descriptions for the maximum idempotent-separated congruences and the minimum group congruences on many kinds of semigroups were given. On the other hand, the class of semigroups with the congruence extension property was involved and described, see [4], [9] and [10]. In this paper, we introduce normalities and invariances for congruences on bands, and discuss that congruences on bands extend to fully regular subsemigroups of Hall semigroups of bands.In addition, we characterize congruences on bands, such as completely invariant congruences and characteristic invariant congruences on bands according to congruence extensions on semigroups, and describe the maximum congruence extension and the minimum congruence extension for a given congruence on a band.