## 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:

$\! F_i(x_1,x_2,\dots,x_n,y_1,y_2,\dots,y_n) = x_i + y_i, 1 \le i \le n$

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.