  We study electron decoherence by measuring the temperature dependence of
Aharonov-Bohm (AB) oscillations in quasi-1D rings, etched in a high-mobility
GaAs/GaAlAs heterostructure. The oscillation amplitude is influenced both by
phase-breaking and by thermal averaging. Thermal averaging is important when
the temperature approaches the energy scale, on which the AB oscillations shift
their phase. For the phase-breaking, it is demonstrated that the damping of the
oscillation amplitude is proportional to the length of the interfering paths.
For temperatures $T$ from 0.3 to 4 $\rm K$ we find the phase coherence length
$\it L_{\phi}$ $\propto$ $T^{-1}$, close to what has been reported for open
quantum dots. This might indicate that the $T^{-1}$ decoherence rate is a
general property of open and ballistic mesoscopic systems.
