  We show, for primes p less than or equal to 13, that a number of well-known
MU_(p)-rings do not admit the structure of commutative MU_(p)-algebras. These
spectra have complex orientations that factor through the Brown-Peterson
spectrum and correspond to p-typical formal group laws. We provide computations
showing that such a factorization is incompatible with the power operations on
complex cobordism. This implies, for example, that if E is a Landweber exact
MU_(p)-ring whose associated formal group law is p-typical of positive height,
then the canonical map MU_(p) --> E is not a map of H_\infty ring spectra. It
immediately follows that the standard p-typical orientations on BP, E(n), and
E_n do not rigidify to maps of E_\infty ring spectra. We conjecture that
similar results hold for all primes.
