  The study of nuclear magnetic resonance and nuclear spin-lattice relaxation
was conducted in an asymmetrically doped to $n\sim1.8\times10^{11}$ cm$^{-2}$
16 nm AlAs quantum well grown in the $[001]$-direction. Dynamic polarization of
nuclear spins due to the hyperfine interaction resulted in the so-called
Overhauser shift of the two-dimensional conduction electron spin resonance. The
maximum shifts achieved in the experiments are several orders of magnitude
smaller than in GaAs-based heterostructures indicating that hyperfine
interaction is weak. The nuclear spin-lattice relaxation time extracted from
the decay of Overhauser shift over time turned out to depend on the filling
factor of the two-dimensional electron system. This observation indicates that
nuclear spin-lattice relaxation is mostly due to the interaction between
electron and nuclear spins. Overhauser shift diminishes resonantly when the
RF-radiation of certain frequencies was applied to the sample. This effect
served as an indirect, yet powerful method for nuclear magnetic resonance
detection: NMR quadrupole splitting of $^{75}$As nuclei was clearly resolved.
Theoretical calculations performed describe well these experimental findings.
