The Dual of a Strongly Prime Ideal

Abstract

Let R be a commutative integral domain with quotient field K and let P be a nonzero strongly prime ideal of R.W e give several characterizations of such ideals. It is shown that (P : P) is a valuation domain with the unique maximal ideal P. We also study when P �1 is ar ing. In fact, it is proved thatP �1 =( P : P) if and only if P is not invertible. Furthermore, if P is invertible, then R =( P : P )a ndP is a principal ideal of R.