Zur Konstruktion faktorieller graduierter Integritätsbereiche
type: Item
instance of: scholarly article
title: Zur Konstruktion faktorieller graduierter Integritätsbereiche
zbMATH Open document ID: 0543.13013
DOI: 10.1007/BF01198127
author: Günter Scheja
author: Uwe Storch
published in: Archiv der Mathematik
publication date: 1984-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 13F15
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 13G05
Mathematics Subject Classification ID: 13A10
zbMATH DE Number: 3863337
zbMATH Keywords: unique factorization domains
zbMATH Keywords: graded Krull domain
zbMATH Keywords: divisor class groups
MaRDI profile type: Publication
cites work: Q3953883
cites work: Q5515450
cites work: Divisorenklassengruppen quasihomogener Singularitäten.
cites work: Q5670698
cites work: Graded factorial rings of dimension 3 of a restricted type
cites work: Q4175678
cites work: Die Picard-Zahlen der Singularitäten = 0
full work available at URL: https://doi.org/10.1007/bf01198127
OpenAlex ID: W2001748011
description: scientific article; zbMATH DE number 3863337