Superpurely simple modules (Q757552)

Let \(\Lambda\) be a tame, hereditary algebra over an algebraically closed field and let Q denote the unique generic \(\Lambda\)-module. A torsion- free \(\Lambda\)-module M is called superpurely simple if every non-zero homomorphism from M to Q is a monomorphism. Such modules arise naturally in the study of infinite dimensional torsion-free purely simple modules. A complete classification of all superpurely simple modules is given. It is shown that there exist only finitely many isomorphism classes of superpurely simple modules of rank greater than one. It is also shown that the number of such modules depends on the orientation which is given to the underlying graph of \(\Lambda\).