Generalized relative primeness in integral domains (Q2891109)

In order to generalize the property of relative primeness to sets of elements of an integral domain \(D\), the authors consider three properties of relations between elements \(a\) and \(b\) of \(D\): \(a\) and \(b\) are comaximal, \(((a,b)^{-1})^{-1}=D\) and the only common divisors of \(a\) and \(b\) are units. The interest in relative primeness lies in factorization, and the authors study domains which admit factorizations of elements into finitely many relatively prime elements according to the various definitions.