半群的Cayley定理

Cayley Theorem in Semi-Groups

利用元素的右乘作用,证明了半群的约半群与一个变换半群同构,由于任一群的约半群是其自己,于是这定理可作为群论中Cayley定理在半群中的推广,并由此得到任一半群的约半群不再可约。

By using right multiplication of elements, in this paper, the authors prove that the reduced semigroup of any semi-group is isomorphic to a transformed semi-group, and that the reduced semi-group of any group is itself. By this reason, the authors generalize Cayley theorem in groups, and finally get the conclusion that the reduced semi-group of any semi-group is irreducible.