 Formal group law

A one-dimensional commutative formal group law over a ring $R$ is a series $F(X,Y)\in R[[X,Y]]$ satisfying the identity, commutativity, and associativity axioms. A homomorphism from $F$ to $G$ is a series $\theta (T)\in TR[[T]]$ satisfying $\theta (F(X,Y))=G(\theta (X),\theta (Y))$.

A formal group law is a mathematical structure that generalizes the notions of group and ring operations in a way that is particularly useful in algebraic topology, algebraic geometry, and number theory. It arises when one studies objects defined over a formal power series ring, and it provides a framework for understanding the behavior of certain types of algebraic operations.