An algorithm for the Traverso-Swan theorem on seminormal rings
type: Item
instance of: scholarly article
title: An algorithm for the Traverso-Swan theorem on seminormal rings
zbMATH Open document ID: 1153.13019
author: Sami Barhoumi
author: Henri Lombardi
published in: Journal of Algebra
publication date: 2008-10-17T00:00:00Z
review text: By Traverso-Swan's theorem a reduced ring \(A\) is seminormal if and only if the canonical map \(\text{Pic } A \rightarrow \text{Pic } A[x]\) is an isomorphism. The necessity could follow also from an algorithm presented in this paper. Let \(C\) be a reduced ring and \(f_1,\ldots, f_n\), \(g_1,\ldots, g_n\) polynomials in \(C[x]\) such that \(\sum_i f_ig_i=1\), \(f_1(0)=g_i(0)=1\), \(f_i(0)=g_i(0)=0\) for \(i>1\). Let \(A\) be the subring of \(C\) generated by the coefficients of the polynomials \(m_{ij}=f_ig_j\), \(1\leq i,j\leq n\) and \(B\) be the subring of \(C\) generated by the coefficients of the polynomials \(f_i,g_i\), \(1\leq i\leq n\). Then \(B\) is the seminormal closure of \(A\) in \(B\).
Mathematics Subject Classification ID: 13F45
Mathematics Subject Classification ID: 13B22
Mathematics Subject Classification ID: 13C10
Mathematics Subject Classification ID: 14C22
Mathematics Subject Classification ID: 13C20
zbMATH DE Number: 5353584
zbMATH Keywords: seminormal ring
zbMATH Keywords: Picard group
zbMATH Keywords: Constructive mathematics
zbMATH Keywords: Traverso-Swan theorem
zbMATH Keywords: Resultant ideal
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2008.05.013
OpenAlex ID: W2076250282
cites work: On seminormality
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cites work: Hidden constructions in abstract algebra. I: Integral dependance.
cites work: A course in constructive algebra
cites work: Q5605674
DOI: 10.1016/J.JALGEBRA.2008.05.013
description: scientific article; zbMATH DE number 5353584