I have an exercise that uses the ring $\mathbb{Z}[1/2]$. I guess are integers but what $\frac{1}{2}$ means?
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Adjoint ring of the ring of integers, $1/2$ is one-half. – Wuestenfux May 08 '19 at 10:13
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Is denotes a ring adjunction. – Bill Dubuque May 08 '19 at 13:43
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It's the ring of the numbers of the form $\frac n{2^m}$, with $n\in\mathbb Z$ and $m\in\mathbb Z^+$. More generally, if $\alpha\in\mathbb C$, then $\mathbb Z[\alpha]$ is the ring of the numbers of the form $a_0+a_1\alpha+\cdots+a_n\alpha^n$, with $a_0,a_1,\ldots,a_n\in\mathbb Z$.
José Carlos Santos
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I believe ${{n\over 2}}$ does not form a ring, since it doesn't contain ${1\over 2}\cdot{1\over 2}={1\over 4}$. – lisyarus May 08 '19 at 10:33
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