On Injective Simple Modules Over a Noetherian Commutative Ring

It is proved in1]that an injective simple module over a noetherian commu-tative ring must be projective.Because every noetherian ring R is a finite directsum of indecomposable rings,say R=R_1(?)…(?)R_n,every simple R-module Smustbe a simple R_i-module for some i and every R-homomorphismσ:M→S must sa-tisfyσ(R_jM)=0(j≠i).Thus it is easy to know theorem2 in1]is equivalentto the following statement which can be proved much easier.