Some Properties Of Prime Essential Rings And Their Generalization

摘要

Prime essential ring and generalized prime essential rings can be used to determine whether a supernilpotent radical is a special radical. Special radical is one of the most important structure in the development of radical theory of rings. Since prime essential rings have an important role in radical theory of rings, we describe some properties of prime essential rings as well as their generalization. We show that every prime essential rings is a subdirectly reducible ring. Furthermore, the prime heart of prime essential ring is zero, so is the semiprime heart of prime an essential ring.