Commutative endomorphism algebras of torsion-free, rank-two Kronecker modules with singular height functions.
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. They show that if the height function never attains infinity then the endomorphism algebra is the ground field \(K\), the square of the ground field or is of the form \(K+S\) with \(S^2=0\). For other height functions, see \textit{F. Okoh} and \textit{F. Zorzitto} [Linear Algebra Appl. 374, 41-62 (2003; see the review Zbl 1044.16022 above)].
scientific article; zbMATH DE number 2012090