Complete Integral Closure and Strongly Divisorial Prime Ideals

Valentina Barucci Dipartimento di Matematica, Università di Roma “La Sapienza”, Piazzale A. Moro, Rome, Italy; Dipartimento di Matematica, Università di Roma “La Sapienza”, Piazzale A. Moro, 5, Rome, 00185, ItalyCorrespondence[email protected]

Stefania Gabelli Dipartimento di Matematica, Università degli Studi Roma Tre, Largo S. L. Murialdo, Rome, Italy

Moshe Roitman Department of Mathematics, University of Haifa, Mount Carmel, Haifa, Israel

Abstract

It is well known that a domain without proper strongly divisorial ideals is completely integrally closed. In this paper we show that a domain without prime strongly divisorial ideals is not necessarily completely integrally closed, although this property holds under some additional assumptions.

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Complete Integral Closure and Strongly Divisorial Prime Ideals

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