关于Oehmke的两个问题

Two Oehmke's Problems

设Ｓ是一个半群，本文主要得到如下几个结果：（１）令Ｔ是Ｓ的一个真子集，Ｔ’是Ｔ左Ｓ中的补集，则；（２）存在Ｓ的子集Ｔ，使得，当且仅当Ｔ＝Ｓ；（３）通过实例说明未必存在子集Ｔ，使得．并给出了有子集Ｔ使得的某一类半群的刻划．

Let S be a semigroup,this paper mainly proves the following results: (1) Let T be a subset of S and T be supplementary subset of T in S,then;(2) There is a subset T of S so that PT= V if T=S;(3) Through some examples,this paper proves that there must not be a subset T of S so that,and gives the description of semigroups with such subsets.