I have the following situation:
Let $R$ be a PID. Then let $\mathfrak{p}\subset R$ be a maximal ideal. We consider the set $$\left(R/\mathfrak{p}\right)[X]$$ which is clearly a quotient, but I would like to know how does equivalence classes (cosets) looks like in this set because I can't imagine this.
It would also be nice if you could give a small explanation why it looks exaclty in this way.
Thank you for your help.