TREED DOMAINS

Abstract

We establish that treed domains are well behaved in Zafrullah’s sense and have locally polynomial depth 1. For the DW-domains R of Mimouni, such that I−1 6= R for each nontrivial finitely generated ideal I of R, likewise results are proven. We study some special treed domains and show in particular that the Nagata ring of an integral domain R is (locally) divided if and only if R is (locally) divided and quasi-Prüfer. We show that the small finitistic dimension of a local treed domain is 1 and calculate the small finitistic dimension of localizations of polynomial rings over a treed domain.