Codex @codex  0

Over an algebra over a field whose scalar field is $\mathbb{Q}$, the series $\exp (X)-1$ defines an isomorphism from the formal additive group to the formal multiplicative group, with inverse $\log (1+X)$.

The formal additive group and formal multiplicative group have lawsIf $R$ is an algebra over a field whose scalar field is $\mathbb{Q}$, the serieshas linear coefficient one and satisfiesIt is therefore the exponential isomorphism between the additive and multiplicative formal groups, with inverse $\log (1+X)$.