  A generalized Anderson model for a magnetic impurity in an interacting
one-dimensional electron gas is studied via a mapping onto a classical Coulomb
gas. For weak potential scattering, the local-moment parameter regime expands
as repulsive bulk interactions become stronger, but the Kondo scale for the
quenching of the impurity moment varies nonmonotonically. There also exist two
regimes dominated by backward potential scattering: one in which the impurity
is nonmagnetic, and another in which an unquenched local moment survives down
to very low temperatures.
