A generalization of conducive domains

Abstract

A domain R is called conducive if every conductor ideal (R:T) is nonzero for all overrings T of R other than the quotient field of R. Let H denote the set of all commutative rings R for which the set of all nilpotent elements forms a divided prime ideal. We extend the concept of conducive domains to the rings in the class H. Initially, we explore the basic properties of ϕ-conducive rings and rings closely related to them. Subsequently, we study these properties in the context of a specific pullback construction and a trivial ring extension.