The purpose of this paper is
to investigate the class of pre-Prüfer rings. A ring is defined to be in this
class in case each of its proper homomorphic images is a Prüfer ring. It
is shown for a domain D that if D is a pre-Prüfer ring, then the prime
spectrum of D forms a tree and every finitely generated ideal of D containing
a bounded element is invertible. If every finitely generated regularizable
ideal of a ring R is invertible, then R is a pre-Prüfer ring. Examples are
presented to show that the converse of each of the two results stated above is
false.
