  The electron-electron interaction quantum correction to the conductivity of
the gated single quantum well InP/In$_{0.53}$Ga$_{0.47}$As heterostructures is
investigated experimentally. The analysis of the temperature and magnetic field
dependences of the conductivity tensor allows us to obtain reliably the
diffusion part of the interaction correction for different values of spin
relaxation rate, $1/\tau_s$. The surprising result is that the spin relaxation
processes do not suppress the interaction correction in the triplet channel
and, thus, do not enhance the correction in magnitude contrary to theoretical
expectations even in the case of relatively fast spin relaxation,
$1/T\tau_s\simeq (20-25)\gg 1$.
