On the wedge product and coprime coalgebras

The wedge product of subcoalgebras of a coalgebra can be used to define coprime coalgebras. On the other hand, coprime elements in the big lattice of preradicals in module categories also lead to the definition of coprime modules. Considering a coalgebra $C$ as a module over its dual algebra $C^{*}$, this yields another notion of coprimeness for coalgebras. Under special conditions, the two definitions coincide.