Definition:Field of Formal Laurent Series

Definition

Let $k$ be a field.

The ring of formal Laurent series $\map k {\paren X}$ over $k$ in a variable $X$ is also called the field of formal Laurent series.

Also denoted as

Since $\map k {\paren X}$ is a field, by Variable of Ring of Formal Laurent Series is Nonzero we may assume $X = Y^{-1}$ is the multiplicative inverse of some element $Y$, and write $\map k {\paren X} = \map k {\paren {Y^{-1} } }$.

Also see

• Ring of Formal Laurent Series over Field is Field