Some polynomial characterizations of Prüfer v-multiplication domains
type: Item
instance of: scholarly article
title: Some polynomial characterizations of Prüfer v-multiplication domains
zbMATH Open document ID: 0541.13007
DOI: 10.1016/0022-4049(84)90053-7
author: Muhammad Zafrullah
published in: Journal of Pure and Applied Algebra
publication date: 1984-01-01T00:00:00Z
review text: Let D be a commutative integral domain. For each non-zero (fractional) ideal A of D, let \(A_ v=(A^{-1})^{-1}\). The ideal B is said to be a v-ideal of finite type if \(B=A_ v\) for some finitely generated A. The set H(D) of such ideals has a multiplication given by \(B.C=B_ vC_ v\), and D is said to be a Prüfer v-multiplication domain if H(D) is then a group. Given a polynomial f in D[X], let \(A_ f\) be the ideal of D generated by the coefficients of f. Let S be the set of polynomials with \((A_ f)_ v=D\). The author's main result is that the following are equivalent when D is integrally closed: (i) D is a Prüfer v-multiplication domain, (ii) \(D[X]_ s\) is Prüfer, (iii) \(D[X]_ s\) is Bezout.
Mathematics Subject Classification ID: 13F05
Mathematics Subject Classification ID: 13F25
zbMATH DE Number: 3859268
zbMATH Keywords: v-ideal
zbMATH Keywords: Prüfer v-multiplication domain
zbMATH Keywords: Bezout
MaRDI profile type: Publication
full work available at URL: 0022-4049(84)90053-7
OpenAlex ID: W2088610237
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description: scientific article; zbMATH DE number 3859268