The distribution of prime divisors in Krull monoid domains
It is well-known that each divisor class of a Krull domain \(D\) contains a height-one prime ideal if either \(D\) is a ring of algebraic integers or \(D\) is a polynomial ring \(R[X]\) where of course \(R\) is a Krull domain. In this paper it is shown that if the monoid domain \(R[S]\) is a Krull domain \((S\) is a torsion-free cancellative monoid) and either \(R\) is a UFD (but not a field) or \(S\) is a group, then each divisor class of \(R[S]\) contains a height-one prime.
scientific article; zbMATH DE number 1563013
scientific article