Formal power series ring

Definition
Let $$R$$ be a commutative unital ring. The formal power series ring over $$R$$ in one variable, denoted $$Rx$$ if the variable (indeterminate) is $$x$$ is the ring whose elements are possibly infinite formal linear combinations of nonnegative integral powers of $$x$$, with addition coordinate-wise and multiplication extended $$R$$-linearly (infinitely so) from a multiplication of powers that adds up the exponents.

Related notions

 * Laurent series ring
 * Puiseux series ring
 * Hahn series ring