  The $\Lambda$-hypernucleus production by $A(p, pK^+)_{\Lambda}B$ reactions is
investigated within the framework of the distorted wave impulse
approximation(DWIA). The amplitude for the elementary process is evaluated in a
fully covariant two-nucleon model based on the effective Lagrangian. The
reaction cross sections for $\Lambda$-hypernucleus productions on $^6Li$,
$^{12}C$ and $^{16}O$ targets are calculated. It is found that the distortion
effects tend to reduce the cross sections by a factor of 3$\sim$10. Various
differential cross sections (DCS) and double differential cross sections (DDCS)
are presented. It is shown that for the $s_{\Lambda}-$wave hypernucleus
production, the DCS is decreased with increasing nuclear mass, and the DCS for
the $p_{\Lambda}-$wave hypernucleus production is normally higher than that for
the $s_{\Lambda}-$wave hypernucleus production. As a reference, the DDCS with
respect to the momenta of the outgoing proton and kaon is also demonstrated.
Finally, the missing mass spectra of the inclusive reaction $p+A\to p+ K^+ + X$
for $^6Li$, $^{12}C$ and $^{16}O$ targets are presented, from which the masses
of hypernuclei can accurately be extracted. Thus, we conclude that the missing
mass spectrum method is an alternative to study hypernuclear physics. And the
study of hypernuclear physics can be carried out in COSY and CSR by the
$A(p,pK^+)_{\Lambda}B$ reaction due to the $\mu$b-order reaction cross
sections.
