  We investigate the pseudogap onset temperature $T^*$, the superconducting
transition temperature $T_c$ and the general nature of the pseudogap phase
using a diagrammatic BCS-Bose Einstein crossover theory. This decoupling scheme
is based on the pairing approximation of Kadanoff and Martin, further extended
by Patton (KMP). Our consideration of the KMP pairing approximation is driven
by the objective to obtain BCS like behavior at weak coupling, (which does not
necessarily follow for other diagrammatic schemes). The breakdown of the Fermi
liquid state at $T^*$ is investigated within the lowest order theory and is
associated with intermediate values of the coupling. The superconducting
instability $T_c$ is evaluated by introducing mode coupling effects, in which
the long lived pairs are affected by the single particle pseudogap states and
vice versa. Our $T_c$ equations, which turn out to be rather simple as a result
of the KMP scheme, reveal a rich structure as a function of $g$ in which the
pseudogap is found to compete with superconductivity. Our results are compared
with alternate theories in the literature.
