  In this paper, we study dot-product sets and $k$-simplices in vector spaces
over finite rings. We show that if $E$ is sufficiently large then the
dot-product set of $E$ covers the whole ring. In higher dimensional cases, if
$E$ is sufficiently large then the set of simplices and the set of dot-product
simplices determined by $E$, up to congurence, have positive densities.
