Regarding the notation $R=\mathbb{Z}[1/N]$, where $N$ is a positive integer, does $R$ refer to:
$R=\{a+b/N|a,b\in\mathbb{Z}\}$
or
$R=\{a_0 +a_1/N+a_2/N^2+\ldots +a_n/N^n|a_i\in\mathbb{Z}\}$
or others?
Thanks a lot.
Regarding the notation $R=\mathbb{Z}[1/N]$, where $N$ is a positive integer, does $R$ refer to:
$R=\{a+b/N|a,b\in\mathbb{Z}\}$
or
$R=\{a_0 +a_1/N+a_2/N^2+\ldots +a_n/N^n|a_i\in\mathbb{Z}\}$
or others?
Thanks a lot.
As the comment suggests it's the second option, where you maybe should specify that $n\in\mathbb N$ may vary. You can think about it differently. Either it's "polynomials" in $\frac 1N$ with coefficients in $\mathbb Z$ or it is the smallest ring which contains $\mathbb Z$ and $\frac 1N$.