ES-w-stability

Abstract

We introduce and study the notion of ES-w-stability for an integral domain R. A nonzero ideal I of R is called ES-w-stable if ðI 2 Þ w ¼ ðJIÞ w for some tinvertible ideal J of R contained in I, and I is called weakly ES-w-stable if I w ¼ ðJEÞ w for some t-invertible fractional ideal J of R and w-idempotent fractional ideal E of R. We define R to be an ES-w-stable domain (resp., a weakly ES-w-stable domain) if every nonzero ideal of R is ES-w-stable (resp., weakly ES-w-stable). These notions allow us to generalize some well-known properties of ES-stable and weakly ES-stable domains.