STRONGLY) π- REGULAR RINGS RELATIVE TO RIGHT IDEAL)

Abstract

In this paper we study the notion of π- regular and strongly π- regular rings relative to right ideal. We provide several characterizations of this rings and study their properties. It is shown that every ring R is π- regular relative to any maximal right ideal of R . Also, we find necessary and sufficient conditions to be a ring R satisfies the d.c.c. on chains of the form Ra ⊇ Ra² ⊇ Λ relative to ideal for every a ∈ R .  New results obtained include necessary and sufficient conditions for a ring to be π- regular, strongly π- regular and P-  potent relative to right ideal.