Additive formal group law

Definition

One-dimensional additive formal group law

Suppose $R$ is a commutative unital ring. The one-dimensional additive formal group law over $R$ is the formal group law given by the power series:

$F(x,y)=x+y$

It is an example of a commutative formal group law.

Higher-dimensional formal group law

Suppose $R$ is a commutative unital ring. The $n$-dimensional additive formal group law over $R$ is the formal group law given by the following collection of power series:

$\!F_{i}(x_{1},x_{2},\dots ,x_{n},y_{1},y_{2},\dots ,y_{n})=x_{i}+y_{i},1\leq i\leq n$

More compactly, this is written as:

$\!F(x,y)=x+y$

where $x=(x_{1},x_{2},\dots ,x_{n})$ and $y=(y_{1},y_{2},\dots ,y_{n})$.

This is an example of a commutative formal group law.