Endomorphism rings of regular modules over wild hereditary algebras

Let X be an indecomposable regular module over a connected wild hereditary path-algebra. The main result is a factorization property for maps in the radical of End(H) (X) and an upper bound for its degree of nilpotency. The bound is sharp if X has elementary quasi-top. In this, case the socle of End(H) (X) can also be characterized.