Rings in which the product of two non-nilpotent elements is non-zero

Abstract

This article studies rings wherein the product of two non nilpotent elements is non zero. We call such rings 'nil domains'. The class of nil domains strictly contains the class of domains and local rings with nil Jacobson radical. We explore and study some ring extensions of nil domain which preserves the nil domain property. Also some consequences of nil domains conditions on some closely related and well known classes of rings are looked into.