  We present a study of the alloying series of the non-centrosymmetric
$f$-electron intermetallic CePt$_3$B$_{1-x}$Si$_x$ by means of muon spin
rotation and relaxation measurements. In addition, we include a high pressure
magnetization investigation of the stoichiometric parent compound CePt$_3$B.
From our data we establish the nature of the magnetic ground state properties
of the series, derive the ordered magnetic moment as function of stoichiometry
and gain insight into the evolution of the symmetry of the ordered magnetic
state with $x$. We thus can verify the notion that the behavior of the sample
series can essentially be understood within the framework of the Doniach phase
diagram. Further, our findings raise the issue of the role the
Dzyaloshinskii-Moriya magnetic interaction plays in correlated electron
materials, and its effect on magnetic fluctuations in such materials.
