The Whitney embedding theorem for tropical torsion modules. Classification of tropical modules
type: Item
instance of: scholarly article
title: The Whitney embedding theorem for tropical torsion modules. Classification of tropical modules
zbMATH Open document ID: 1221.15037
author: Edouard Wagneur
published in: Linear Algebra and its Applications
publication date: 2011-07-13T00:00:00Z
review text: The author proves a tropical version of the well-known Whitney embedding theorem [\textit{H. Whitney}, Ann. Math. (2) 45, 220--246 (1944; Zbl 0063.08237)]. The tropical version states that a tropical torsion module with \(m\) generators can be embedded into the free tropical module \(\mathbb{R}^p\), where \(p\) (equals \(2\) for \(m=2\) and \(3\leq p\leq m(m-1)\) otherwise) is the number of rows supporting the torsion, when the generators are given by the (independent) columns of a matrix of size \(n\times m\). As a corollary, the tropical \(m\)-dimensional torsion modules are classified by an \((m-1)(m(m-1)-1)\)-parameter family.
Mathematics Subject Classification ID: 15A80
Mathematics Subject Classification ID: 16D80
Mathematics Subject Classification ID: 15A39
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 16D40
zbMATH DE Number: 5919626
zbMATH Keywords: max algebra
zbMATH Keywords: tropical algebra
zbMATH Keywords: tropical module
zbMATH Keywords: torsion matrix
zbMATH Keywords: Whitney embedding theorem
reviewed by: Andreas Arvanitoyeorgos
MaRDI profile type: Publication
full work available at URL: j.laa.2011.02.034
OpenAlex ID: W2077259161
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DOI: 10.1016/J.LAA.2011.02.034
description: scientific article; zbMATH DE number 5919626