How do I talk about the elements of $\Bbb Z{\left[\frac16\right]}$ in the interval $\left[\frac23,\frac43\right)$ as a set with addition reduced by $\frac23$?
It would seem to be a torsion group with identity $\frac23$ and I imagine would most likely be thought of in the interval $\left[0,\frac23\right)$ with identity $0$, but I don't even know how to write that.
My effort would be say $\frac23+\left(\Bbb Z[\frac16]/\frac23\Bbb Z\right)$ but that's a wild stab in the dark to be fair.
What would be standard or common terminology for this, if there is any (and am I right in thinking it's a quotient group)?