П正则半群的幂等元同余类

THE CONGRUENCE CLASS OF AN IDEMPOTENT IN A П REGULAR SEMIGROUP

本文分别给出П正则半群的幂等元同余类和Пｏｒｔｈｏｄｏｘ半群［１］的幂等元同余类的П正则性刻画．其次，证明П逆半群或完全П正则半群Ｓ的幂等元同余类是Ｓ的П正则子半群．最后讨论ｏｒｔｈｏｄｏｘ半群的幂等元同合类的正则性．

In this paper,at the first it is characterized for the congruence class of an idempotent in a H regular or H orthodox semigroup which is a H regular subsemigroup of S, respectively. Then we prove that the congruence class of an idempotent in a inverse or completely regular semigroup is H regular. Finally, we discuss the regular property of the congruence class of an idempotent in a arthodox semigroup.