Zur Konstruktion faktorieller graduierter Integritätsbereiche
Generalizing a result of \textit{P. Samuel} [''Lectures on unique factorization domains'' (Tata Institute 1964; Zbl 0184.066)] the following is proved: Let A be a (not necessarily positively) graded Krull domain and \(f\in A\) be a homogeneous element \(\neq 0\) of degree \(m>0\) such that Af is the intersection of \(t\geq 0\) different prime ideals of codimension 1. Let n be a positive number relatively prime to m. Then the free algebra \(B:=A[Z]/(Z^ n-f)\) over A is a Krull domain, the canonical homomorphism \(Cl(A)\to Cl(B)\) of divisor class groups is injective, the cokernel being isomorphic to the direct sum of max(0,t-1) copies of the cyclic group of order n. - The proof is elementary and depends on an interpretation of a construction by P. Samuel (loc. cit.). Several examples and applications are given.
scientific article; zbMATH DE number 3863337