Additive formal group law

One-dimensional additive formal group law
Suppose $$R$$ is a commutative unital ring. The one-dimensional additive formal group law over $$R$$ is the defining ingredient::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 defining ingredient::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.