Let A be a Mori domain. We show here that the complete integral closure A* is completely integrally closed provided A is seminormal and that A** is always completely integrally closed. On the other hand, in general A* need be neither completely integrally closed nor Mori. In order to obtain such examples we define and study power functions.
Bibliographical noteFunding Information:
This work was partly supported by Consiglio Nazionale delle Ricerche (Italy) while enjoying the hospitality of Universita di Roma ‘La Sapienza’. Discussions with Professors Valentina Barucci, Marco Fontana and Stefania Gabelli were very useful. The seminormality assumption (rather than root closure) in Section 1 is due to Professor David F. Anderson (University of Tennessee, Knoxville). I thank Professor Jonathan S. Golan (University of Haifa) for his remarks. The main results of this paper were presenteda t Journees d’algebre commutative -Lyon 1988.
ASJC Scopus subject areas
- Algebra and Number Theory