Splitting the t-class group (Q1181495)

The aim of the paper is to generalize the following well known theorem of Nagata: ``If \(D\) is a Krull domain and \(S\) a multiplicative subset generated by prime elements, then the divisor class groups of \(D\) and \(D_ S\) are canonically isomorphic.'' Here \(D\) is an arbitrary domain. Instead of the monoid of divisorial ideals the monoid of so named \(t\)- ideals is considered. (These notions coincide in Krull-domains.) For special \(S\) the authors get a splitting of this monoid and also one of the class groups of ``\(t\)-invertible \(t\)-ideals''.