This paper concerns just when analogues of vn can occur in ring spectra
besides BP.  There is a sort of general theory, and then there are
applications.  Most of the applications concern v1 elements in bordism
spectra like MO8.  Basically v1 elements exist when elements in the
image of J go to 0 under the unit map.  We determine just which elements
in the image of J survive in the homotopy of bordism spectra MOk, and
thereby construct v1 elements.