Editing Signed-digit representation (section)

====Prüfer groups====
A [[Prüfer group]] is the [[quotient group]] <math>\mathbb{Z}(b^\infty) = \mathbb{Z}[1\backslash b]/\mathbb{Z}</math> of the integers and the <math>b</math>-adic rationals. The set of all signed-digit representations of the [[Prüfer group]] is given by the [[Kleene star]] <math>\mathcal{D}^*</math>, the set of all finite [[concatenation|concatenated]] strings of digits <math>d_{1} \ldots d_{n}</math>, with <math>n\in\mathbb{N}</math>. Each signed-digit representation <math>p \in \mathcal{D}^*</math> has a [[Valuation (algebra)|valuation]] <math>v_\mathcal{D}:\mathcal{D}^*\rightarrow\mathbb{Z}(b^\infty)</math>
:<math>v_\mathcal{D}(m) \equiv \sum_{i=1}^{n}f_\mathcal{D}(d_{i})b^{-i} \bmod 1</math>