*This post assumes familiarity with formal group laws, the definition of exact sequences, the motivation of the Landweber-Ravenel-Stong construction, that the exactness axioms is one of the generalized Eilenberg-Steenrod axioms, and the fact that formal group laws over $R$ are represented by maps from the Lazard ring to $R$. *

Recall the the Landweber-Ravenel-Stong Construction: $MU^*(X) \otimes_{L} R \simeq E^*(X)$, where $MU^* \simeq L$ and $R \simeq E^*(pt)$.

*We know that in general, tensoring with abelian groups does not preserve exact sequences (**e.g., applying $-\otimes_{\mathbb{Z}} \mathbb{Z}/2$ to $0 \to \mathbb{Z} \xrightarrow{\times p} \mathbb{Z} \to \mathbb{Z}/p \to 0$). *

So, when does the functor $-\otimes_L R: MU^*(X) \to E^*(X)$ preserve exact sequences?