A Direct Proof of a Theorem concerning Treed Overrings

الملخص EN

We improve and provide a direct proof of a theorem that answered a question by Dobbs about treed overrings.

More precisely, we show that if R is an integrally closed local domain and each of its proper overrings is treed, then R is a valuation domain or R is a PVD with associated valuation overring V such that tr.deg[V/M:R/M]=1.