Multiplicative formal group law

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

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

It is an example of a commutative formal group law.

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

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

This is an example of a commutative formal group law.