Study on prime and semi-prime goldie rings and modules

Abstract

Let R be a ring. Then the ring R has finite right Goldie dimension if it contains a direct sum of a finite number of nonzero right ideals. Symbolically, we write G.dim(R)  . A ring R is called a right Goldie ring if it has finite right Goldie dimension and satisfies the ascending chain condition (ACC) for right annihilators. A module M is called a Goldie module if it has finite Goldie dimension and if it satisfies the ACC on M-annihilator submodules. In this thesis, we develop some properties of prime and semi-prime submodules over associative endomorphism rings by modifying the properties of prime and semi-prime ideals over associative arbitrary rings. Also, we investigate some properties of prime and semi-prime Goldie modules over associative endomorphism rings. .