Abstract:
In this project, we use the notion of totally fully invariant right (left) ideal to define the ring whose prime right (left) ideals are totally fully invariant. This ring is called a prime right (left) strongly quasi-duo ring. We investigate some properties of a prime right strongly quasi-duo ring. Moreover, we are interested in studying the ideal J*(R) of a prime right strongly quasi-duo ring R which is the intersection of all prime right ideals of R. We find that if R is a hereditary and a prime right strongly quasi-duo ring, then R/J*(R) is a prime right strongly quasi-duo ring. Finally, we study zero divisors in an arbitrary ring, in a prime right strongly quasi-duo ring and in a prime left strongly quasi-duo ring.
