Commutative algebras of rational function matrices as endomorphisms of Kronecker modules. I.
type: Item
instance of: scholarly article
title: Commutative algebras of rational function matrices as endomorphisms of Kronecker modules. I.
zbMATH Open document ID: 1044.16022
DOI: 10.1016/S0024-3795(03)00539-1
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 describe the endomorphism algebras of all the indecomposable modules depending on how the height function looks like.
reviewed by: Gábor Braun
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 15A27
Mathematics Subject Classification ID: 16W20
zbMATH DE Number: 2005992
zbMATH Keywords: rank 2 Kronecker modules
zbMATH Keywords: height functions
zbMATH Keywords: regulating polynomials
zbMATH Keywords: endomorphism algebras
MaRDI profile type: Publication
cites work: Q4318498
cites work: On Algebraic Equivalence Between Pairs of Linear Transformations
cites work: Q4513600
cites work: Embeddings of Kronecker modules into the category of prinjective modules and the endomorphism ring problem
cites work: Rigid families and endomorphism algebras of Kronecker modules
cites work: Q3310781
cites work: A class of infinite-rank modules over tame hereditary algebras
cites work: A family of commutative endomorphism algebras
cites work: Curves arising from Kronecker modules.
cites work: Commutative endomorphism algebras of torsion-free, rank-two Kronecker modules with singular height functions.
cites work: Q3866236
cites work: Q2702060
cites work: Q4271281
description: scientific article; zbMATH DE number 2005992