Torsion-free modules over reduced Witt rings
type: Item
instance of: scholarly article
title: Torsion-free modules over reduced Witt rings
zbMATH Open document ID: 0961.11017
author: Robert W. Fitzgerald
published in: Journal of Algebra
publication date: 2001-05-24T00:00:00Z
full work available at URL: https://opensiuc.lib.siu.edu/math_articles/29
review text: For a ring-order \(R\), \textit{R. Wiegand} and \textit{R. Guralnick} [Lect. Notes Pure Appl. Math. 189, 333-347 (1997; Zbl 0884.13004)] defined the genus class group Genus(\(M\)) of a torsion-free, finitely generated \(R\)-module \(M\). The goal of the paper under review is to show that some of these results also hold for the reduced Witt rings of finite stability index. This generalizes previous results of the author on projective modules over Witt rings [J. Algebra 183, 286-305 (1996; Zbl 0922.11036)] to a wider class of modules. The main objects of interest are odd degree field extensions \(K\) of a formally real field \(F\) with finite stability index. The results of the paper apply to \((WK)_{\text{red}}\) considered as a \((WF)_{\text{red}}\)-module.
reviewed by: Andrzej Sładek
Mathematics Subject Classification ID: 11E81
Mathematics Subject Classification ID: 12D15
Mathematics Subject Classification ID: 13C10
Mathematics Subject Classification ID: 13C20
zbMATH DE Number: 1526437
zbMATH Keywords: Witt ring
zbMATH Keywords: reduced Witt ring
zbMATH Keywords: stability index
zbMATH Keywords: ring-order
zbMATH Keywords: genus class
zbMATH Keywords: conductor
MaRDI profile type: Publication
OpenAlex ID: W2092986355
cites work: Quadratic Forms Over Formally Real Fields and Pythagorean Fields
cites work: Q4182814
cites work: Primary ideals in Witt rings
cites work: Picard groups of Witt rings
cites work: Projective modules over Witt rings
cites work: Q4343552
cites work: Commutative orders whose lattices are direct sums of ideals
cites work: Q3663392
cites work: Q3897105
cites work: Rings of Integer-Valued Continuous Functions
cites work: Q3708857
cites work: Cancellation over commutative rings of dimension one and two
cites work: Stable isomorphism of modules over one-dimensional rings
DOI: 10.1006/JABR.1999.8374
Recommended article: Q3215376
Recommended article: Torsion free modules
Recommended article: Q4301750
Recommended article: Q3682631
Recommended article: Torsionfree modules over one-dimensional Noetherian rings
Recommended article: SOME RESULTS ON TORSIONFREE MODULES
Recommended article: On torsion free distributive modules
Recommended article: Torsion-Free and Divisible Modules Over Finite-Dimensional Algebras
Recommended article: n-T -torsionfree modules
Recommended article: Q5307889
description: scientific article; zbMATH DE number 1526437