Recent years have witnessed a significant development of the theory of Prüfer domains; there are many known characterizations of such domains within the class of integral domains with identity or the class of integrally closed domains—for example, see [6; Exer. 12, p. 93] or [10; Chap. 4]. E. Bastida and R. Gilmer have recorded in  a number of open questions concerning Prüfer domains that are of the following form:
If D is an integral domain with identity with property E, is the integral closure of D a Prüfer domain?
Specifically, the questions listed by Bastida and Gilmer were first raised in , , , and .