Can someone please tell me what the group $\displaystyle \mathbb{Z}[1/n]$ is?
Never mind - I was having a dull moment. If you are interested, it is just the integers in another guise...
Can someone please tell me what the group $\displaystyle \mathbb{Z}[1/n]$ is?
Never mind - I was having a dull moment. If you are interested, it is just the integers in another guise...
Well, not precisely...if $\displaystyle n=2$ , for example, and since the notation $\displaystyle \mathbb{Z}[1\slash n]$ usually denotes the set of all the values $\displaystyle p(1\slash n)\,,\,\,with\,\,\,p(x)\in\mathbb{Z}[x]$ , then
with $\displaystyle p(x)=x$ we obtain $\displaystyle p(1\slash 2)=1\slash 2\notin\mathbb{Z}$ , so in fact $\displaystyle \mathbb{Z}[1\slash n]\neq \mathbb{Z}$
Tonio