Commutative algebras of rational function matrices as endomorphisms of Kronecker modules. II.
type: Item
instance of: scholarly article
title: Commutative algebras of rational function matrices as endomorphisms of Kronecker modules. II.
zbMATH Open document ID: 1044.16023
DOI: 10.1016/S0024-3795(03)00538-X
author: Frank Okoh
author: Frank A. Zorzitto
published in: Linear Algebra and its Applications
publication date: 2003-11-19T00:00:00Z
review text: A Kronecker module is a pair of modules \(U\) and \(V\) together with two homomorphisms from \(U\) to \(V\). The authors study the endomorphism algebras of indecomposable Kronecker modules over an algebraically closed field \(K\) which are extensions of finite dimensional torsion-free rank 1 modules by infinite dimensional torsion-free rank 1 modules. The infinite dimensional rank 1 module in the extension is characterized by a height function, a function which maps the elements of \(K\) and infinity to a non-negative integer or infinity. The authors prove that if the height function is constant infinity and the characteristic of the ground field \(K\) is not 2 then the endomorphism algebra is just \(K\). For other height functions, see part I [the authors, Linear Algebra Appl. 374, 41-62 (2003; see the review Zbl 1044.16022 above)].
reviewed by: Gábor Braun
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 15A27
Mathematics Subject Classification ID: 16W20
zbMATH DE Number: 2005993
zbMATH Keywords: rank 2 Kronecker modules
zbMATH Keywords: height functions
zbMATH Keywords: regulating polynomials
zbMATH Keywords: endomorphism algebras
MaRDI profile type: Publication
cites work: Q4513600
cites work: Rational functions and kronecker modules
cites work: The pure-projective dimension of torsion-free divisible modules
cites work: Q4254917
cites work: A family of commutative endomorphism algebras
cites work: Commutative algebras of rational function matrices as endomorphisms of Kronecker modules. I.
cites work: Q3866236
full work available at URL: s0024-3795(03)00538-x
OpenAlex ID: W4245666795
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description: scientific article; zbMATH DE number 2005993