On Krull overrings of a Marot ring whose regular ideals are finitely generated

Let R be a Marot ring whose regular ideals are finitely generated and D a K rull overring of R. In this paper, we show that if reg-dimR less than or eq ual to 2, then each regular ideal of D is finitely generated and reg-dimD l ess than or equal to 2. In particular, each regular ideal of a Krull overri ng of a Noetherian ring R is finitely generated provided that (regular) Kru ll-dimension R less than or equal to 2. This is a generalization of the wel l-known fact that a Krull overring of a Noetherian domain with Krull-dimens ion less than or equal to 2 is also a Noetherian domain with Krull-dimensio n less than or equal to 2.