A criterion for pure simplicity (Q915833)

This paper deals with the problem of detecting whether or not a Kronecker module is purely simple. The authors prove that for each finite- dimensional torsion-free module N by an infinite-dimensional torsion-free module F of rank 1 a purely simple Kronecker extension module M does exist. Extensions of N by F are built up using linear functionals on K(X), the space of rational functions. The authors' existence proof is based on a criterion in terms of such functionals for the pure simplicity of an extension M. The paper is started with the sections on introduction and preliminaries, then the authors begin to search for a usable criterion for detecting when a module in \(\epsilon_{n+1}\) is purely simple. The paper is ended with a section of embedding and reduction.