Semirigid GCD domains

Let R be a commutative integral domain. An element x of R is calledrigid if for all r,s dividing x; r divides s or s divides r. In our terminology, R issemirigid if each non zero non unit of R is a finite product of rigid elements. We show that semirigid GCD domains have a type of unique factorization, and are a known generalization of Krull domains.