  We show the uniqueness and existence of the Euler form for a simply-laced
generalized root system. This enables us to show that the Coxeter element for a
simply-laced generalized root system is admissible in the sense of
R.~W.~Carter. As an application, the isomorphism classes of simply-laced
generalized root systems with positive definite Cartan forms are classified by
Cartar's admissible diagrams associated to their Coxeter elements.
