Journal of the
Korean Mathematical Society JKMS

Ravenel computed the Adams spectral sequence converging to $BP_{*}(\Omega^{2}S^{2n+1})$ and got the $E_{\infty}$--term. Then he gave the conjecture about the extension. Here we prove that there should be non--trivial extension. We also study the $BP_{*}BP$ comodule structures on the polynomial algebras which are related with $BP_{*}(\Omega^{2}S^{2n+1})$.

Keywords: Adams spectral sequence, Brown--Peterson homology, extension problem

MSC numbers: 55N22, 55T15