Set of rational numbers having denominator $D$ The set of rational numbers is customarily denoted $\mathbb{Q}$. I need a symbol for the set of rational numbers having denominator $D$. For example, for $D = 3$, this set would be
$$\{ \cdots, -4/3, -3/3, -2/3, -1/3, 0/3, 1/3, 2/3, 3/3, 4/3, \cdots \}.$$
I am considering adopting the notation $\mathbb{Q}_D$, but I wanted to ask if there is a standard or more widely recognized symbol for this set.

*

*If so, what is it?

*If not, what symbol should I use?

*Is it necessary to clarify explicitly that my set includes rational numbers in "unsimplified" form (e.g. $3/3$ in the example above)?

 A: The notation $\,n\mathbb Z\,$ used for integer multiples of $\,n\,$ could suggest a symmetrical notation $\,\mathbb Z/n\,$ for rational fractions with denominator $\,n\,$. This would also make it clear that the numerator is unrestricted, so the set would include fractions where a common factor might cancel out, for example $\,\frac{n}{n} = 1 \in \mathbb Z /n\,$.
One problem with this notation is that, in certain contexts at least, it would conflict with the traditional use of $\,\mathbb Z / I\,$ for quotient groups (or rings). In simple cases, the ambiguity could be resolved from the context alone, for example $\,\mathbb Z / 3\,$ could only mean the set of fractions with denominator $\,3\,$, while $\,\mathbb Z / 3\mathbb Z\,$ could only mean the ring of integers $\bmod 3\,$. However, this wouldn't always work in more complex cases, for example $\,\mathbb Z[x]/(x^2+1)\,$ could mean either the set of rational functions with denominator $\,x^2+1\,$ and the numerator a polynomial with integer coefficients, or the ring of polynomials $\,\bmod (x^2+1)\,$.
The notation could maybe use a symbol other than "$/$" to disambiguate, for example $\,\frac{\mathbb Z}{3}\,$ or $\,\mathbb Z \div 3\,$, though neither look too "natural".
