  The one-dimensional Ising model in an external magnetic field with uniform
long-range interactions and random short-range interactions satisfying bimodal
annealed distributions is studied. This generalizes the random model discussed
by Paladin et al. (J. Phys. I France 4, 1994, p. 1597). Exact results are
obtained for the thermodynamic functions at arbitrary temperatures, and special
attention is given to the induced and spontaneous magnetization. At low
temperatures the system can exist in a ``ferrimagnetic'' phase with
magnetization 0<m<1, in addition to the usual paramagnetic, ferromagnetic and
antiferromagnetic phases. For a fixed distribution of the random variables the
system presents up to three tricritical points for different intensities of the
long-range interactions. Field-temperature diagrams can present up to four
critical points.
