Let $R$ be a ring and $R((x))$ the ring of formal Laurent series. The elements in the ring $R((x))$ are series of the form $$ f = \sum_{n\in\mathbb{Z}} a_n X^n, $$ where ${\displaystyle a_{n}=0}$ for all but finitely many negative indices $n$.

The spectrum of a ring is the set of all prime ideals of in the ring.

What is the spectrum of $R((x))$? Thank you very much.

Let $R$ be a ring and $R((x))$ the ring of formal Laurent series. The elements in the ring $R((x))$ are series of the form $$ f = \sum_{n\in\mathbb{Z}} a_n x^n, $$ where ${\displaystyle a_{n}=0}$ for all but finitely many negative indices $n$.

The spectrum of a ring is the set of all prime ideals of in the ring.

What is the spectrum of $R((x))$? Thank you very much.

Edit: Assume that $R$ is a field.