Commutative Ring Theory

1 Seminormal Mori Domains

VALENTINA BARUCCI Dipartimento di Matematica, Università di Roma ‘La Sapienza’, P.le A. Moro, 2-00185 Roma, Italy

Introduction

A Mori domain is a domain such that the ascending chain condition holds for integral divisorial ideals. Thus the first examples of Mori domains are Noetherian domains. It is well known that a completely integrally closed Mori domain is a Krull domain . However, as M.Roitman has shown, the complete integral closure A^* of a Mori domain A is not necessarily a Krull domain. Indeed A^* need be neither completely integrally closed nor Mori (cf.[R]).The main result of this paper is the following: if A is a seminormal Mori domain, then A^* is a Krull domain.

Recall that a domain A is seminormal if, for ...