Study on rings whose prime right ideals are totally fully invariant

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.