TORSION THEORIES AND PRIMARY DECOMPOSITION OF MODULES

In this paper,the author obtains the following result:If R is a left semi-artinian maxring,then the primary decomposition theorem holds for all R-modules if and only if Ext(S_1,S_2)=0 for any non-isomorphic simple modules S_1 and S_2.By mecns of the primarydecomposition of modules,the author proves:All torsion theories of ~Bμ are simple type ifand only if R isa left semi-artinian max ring and Ext(S_1,S_2)=0 for any non-isomorphicsimple modules S_1,S_2.