Computing the extensions of preinjective and preprojective Kronecker modules

JOURNAL OF ALGEBRA

卷:408

Article

Szoellosi, Istvan

关键词: Kronecker algebra;    Matrix pencil;    Preinjective Kronecker module;    Preprojective Kronecker module;   

DOI  :  10.1016/j.jalgebra.2013.09.003

来源: Elsevier

【 摘 要 】

Let I, I' be preinjective Kronecker modules (i.e. all their indecomposable components are preinjective). We describe the modules M for which there exists an exact sequence 0 -> I'-> M -> I -> 0 by explicit, easy to check numerical conditions, resulting in an algorithm (linear in the number of indecomposable components) for the decision problem. We also propose a method to generate all extensions of I' by I and we give a different proof for a theorem in [13] providing numerical criteria in terms of Kronecker invariants for the existence of a monomorphism f : I'-> I. All these results apply dually to preprojective modules as well. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free