Let $R$ be a ring and $R((x))$ the ring of [formal Laurent series](https://en.wikipedia.org/wiki/Formal_power_series#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.



What is the spectrum of the ring $R((x))$ of formal Laurent series over a ring $R$?
If $R$ is a field, then the same page that you link to states that [$R((x))$ is a field](https://en.wikipedia.org/wiki/Formal_power_series#Formal_Laurent_series), too - in fact, it is the field of fractions of the ring $R[[x]]$ of formal series. Since it is a field, its only ideals are $0$ and $R((x))$ - of which, by convention, [only $0$ is considered prime](https://en.wikipedia.org/wiki/Prime_ideal#Prime_ideals_for_commutative_rings). Therefore, the spectrum of $R((x))$ when $R$ is a field is reduced to a single point.


