This paper uses exponential sum methods to show that if \(E \subset \mathcal (\mathbb{Z}/p^r)^n \setminus (p)^{(n)}\) has a sufficiently large density and \(j\) is any unit in the finite ring \(\mathbb{Z}/p^r\) then there exist pairs of elements of \(E\) whose dot product equals \(j\). It then applies this to the problem of detecting \(2-\) simplices with endpoints in \(E\).