Semisimple (simple) module and length property

Abstract

The notion of length module was introduced by Lomp (1999) because of utmost importance to the topic of finite length we should be exposed of some modules which it is related to this property. In this article we introduce new conditions over semisimple, simple modules and we discuss some of the basic characterizations of these modules which show many relations between these module and length property. Since any weakly supplemented module with zero radical is semisimple then hdim(M )=length(M ) holds. Therefore supplemented and hollow modules are weakly supplemented with Rad (M )=0 implies hdim(M)=length(M ), therefore since semisimple module is direct sum of simple submodule then any simple module have finite length property.