FCP Delta -extensions of rings

Abstract

We consider ring extensions, whose set of all subextensions is stable under the formation of sums, the so-called Delta -extensions. An integrally closed extension has the Delta -property if and only it is a Prüfer extension. We then give characterizations of FCP Delta -extensions, using the fact that for FCP extensions, it is enough to consider integral FCP extensions. We are able to give substantial results. In particular, our work can be applied to extensions of number field orders because they have the FCP property.