P-反演半群上由超迹决定的最小强P-同余

Minimum Strong P-congruences Determined by Hyper Trace on P-inversive Semigroups

P-反演半群类是十分重要的一类与正则半群有较密切联系的半群类.关于该类半群的结构及同余受到国内外众多半群工作者的广泛关注.研究了P-正则半群的强P-同余格中一类极小的同余,引入了特征子半群及超迹的概念,借助于同余理论刻画了P-反演半群S(P)上的强P-同余.确定了与给定同余有相同超迹的最小强P-同余,并给出了由超迹决定的最小强P-同余的一种具体表示.这些结果推广了正则半群上的相应结果.

The class of P-inversive semigroups is a very important one,which is closely linked with the well-known class of regular semigroups.The structures and congruences about P-inversive semigroups are widely studied by numerous domestic and international semigroup workers.In this paper,we study a class of tiny congruences in the strong P-congruence lattices of P-regular semigroups.The concepts of characteristic subsemigroups and hyper traces are introduced and the strong P-congruence on P-inversive semigroups S（P） is investigated in terms of congruence theory.The minimum strong P-congruence whose hyper trace coincide with the hyper trace of given congruence is described and a specific description is presented.These results generalize the corresponding results for regular semigroups.