关于内射模的几个注记(Ⅱ)

SOME REMARKS ON INJECTIVE MODULES (Ⅱ)

借助于内射模的性质，证明如下主要结果：１）若内射Ｒ模的每个子模内射，则Ｒ是遗传环；２）若环Ｒ的每个循环左Ｒ模投射，则Ｒ是半单环；

Using the properties of injective modules, the following main results are showed: 1) If all submodules of every injective R module are injective modules, then R is a hereditary ring; 2) If all cyclic left R modules are projective, then R is a semisimple ring; 3) Every submodule of flat module over a hereditary is flat.