Some Studies On The Radicals And Socles Of Modules

In this paper, three points are chie?y discussed.â… We study the properties of radical super?uous modules (RS modules forabbreviation ) and socle essential rings, and discuss the relationship between theRS modules and Bass modules. At the same time, we do some characterizationson Bass ring and semiartinian ring.â…¡We introduce the notion of soc-projective modules and rad-projectivemodules and study the equivalent characterizations and properties of soc-projective modules and rad-projective modules. In addition, we use soc-projective modules to character semisimple rings, PS rings, etc; we use rad-projective modules to character J-semisimple rings, etc. At last, we get a equalstatement on a SF ring is a Von Nemann regular ring.â…¢We introduce the concept of soc-?at modules and the homological di-mension of soc-?at modules, and get some properties of soc-?at modules andthe homological dimension of soc-?at modules. At last, we get a generalizationof Chase's theory by soc-?at modules.