  A short proof of the generalized Riemann hypothesis (gRH in short) for zeta
functions $\zeta_{k}$ of algebraic number fields $k$ - based on the Hecke's
proof of the functional equation for $\zeta_{k}$ and the method of the proof of
the Riemann hypothesis derived in [$M_{A}$] (algebraic proof of the Riemann
hypothesis) is given. The generalized Riemann hypothesis for Dirichlet
L-functions is an immediately consequence of (gRH) for $\zeta_{k}$ and suitable
product formula which connects the Dedekind zetas with L-functions.
