2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66567It is well known that a domain without proper strongly divisorial ideals is completely integrally closed. In this paper we show that a domain without {\em prime} strongly divisorial ideals is not necessarily completely integrally closed, although this property holds under some additional assumptions.18 pagesCommutative Algebra13A15; 13G05; 13B22text