Formal power series ring
Definition
Let be a commutative unital ring. The formal power series ring over in one variable, denoted if the variable (indeterminate) is is the ring whose elements are possibly infinite formal linear combinations of nonnegative integral powers of , with addition coordinate-wise and multiplication extended -linearly (infinitely so) from a multiplication of powers that adds up the exponents.
![{\displaystyle R[[x]]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5aacb21250f99f332a57763ecb7f92e3637ade19)
