Rational functions and kronecker modules

There exists a function f: K → K, on any infinite field K, such that for any rational function r(X), f and r agree on a finite but not empty set. The purely simple modules of rank two over the Kronecker algebra may be all indexed by three parameters: a positive integer n, a height function and a K-linear map α: K(X) → K. When the support of h,i.e. { θ ε K: h(θ) ≥ 0}, has lesser cardinality than K,then the integer n is redundant. If the support of hhas the same cardinality as K, then for each there exists a purely simple, rank two, A-module E(n,h,α),not isomorphic to any other purely simple module of rank two, which is indexed by a positive integer less than n. The construction of this E(n,h,α) uses the function f.