This paper introduces a class of domains which we hope to show merits some attention.

Definition. The domain R is said to be a distinguished domain if for any 0 ≠ z ∈ K, the quotient field of R, (1 : z) does not consist entirely of zero divisors modulo (1 : z–l). (Note: Here we use the fact that a zero module has no zero divisors. Thus if z–l ∈ R, so that (1 : z–l) = R, then the condition holds trivially.)

Section 1 of this paper gives numerous examples of distinguished domains, foremost among them being Krull domains and Prufer domains. In fact Prüfer domains are shown to be exactly those distinguished domains whose prime lattice forms a tree. Other distinguished domains can be constructed by the D + M construction. It is shown that distinguished domains are integrally closed but the converse fails.