关于周期矩形群的一个等价刻划

An Equal Complement About Periodic Rectangular Groups

本文证明了如下的结论：设半群Ｓ＝Ｒ×Ｌ是半群Ｒ与Ｌ的直积，则对Ｓ的任一子半群Ｔ，都存在Ｒ与Ｌ的子半群Ｒ’和Ｌ’，使得Ｔ＝Ｒ’×Ｌ’，当且仅当Ｓ是一矩形带与一周期群的直积．

The article has proved the conclusion as follows:Let sernigroup S =R×L is direct product of semigroup R and L. then for all subsemigroup T of S, there exists subsemigroup Rf and L' of R and L, such that T=R'× L',if and only if S is the direct product of a rectangular band and a periodic group.