  We present the quantum phase diagram of the one-dimensional $t$-$J_z$ model
for arbitrary spin (integer or half-integer) and sign of the spin-spin
interaction $J_z$, using an {\it exact} mapping to a spinless fermion model
that can be solved {\it exactly} using the Bethe ansatz. We discuss its
superconducting phase as a function of hole doping $\nu$. Motivated by the new
paradigm of high temperature superconductivity, the stripe phase, we also
consider the effect the antiferromagnetic background has on the $t$-$J_z$ chain
intended to mimic the stripe segments.
