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.
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