I've found a few articles that write the ring of formal Laurent series in $t$ as $R((1/t))$, but what's the underlying meaning of $\cdot ((\cdot))$?


A mathematician of my acquaintance swears that $R((t))$, not $R((1/t))$, should be used to denote the ring of formal Laurent series in $t$. We can't decide who's right without knowing what $\cdot((\cdot))$ means. (We both agree that $R[[t]]$ denotes the ring of formal power series in $t$ with coefficients in $R$.)



notation for formal Laurent series
I agree with the mathematician of your acquaintance -- well, okay, I am the mathematician of your acquaintance.


Here are some references for the notation $K((x))$ for the field of formal Laurent series $\sum\_{n \geq n\_0} a\_n x^n$ over $K$:



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> The [wikipedia article on formal power series](http://en.wikipedia.org/wiki/Formal_Laurent_series#Formal_Laurent_series).
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> Jacobson's *Basic Algebra II*, $\S 9.12$.
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> Lam's *Introduction to Quadratic Forms Over Fields*, $\S VI.1$
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> Neukirch's *Algebraic Number Theory*, $\S II.4$.
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> Serre's *Corps Locaux*, $\S 1.1$.
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