I am not sure what is the right phrase for primes in some ring. The definition I was gave is that in a ring $A$, $p\in A$ is prime if $\forall x,y \in A$ such that $p\mid xy$, $p\mid x$ or $p\mid y$.
I don't know how to start.(I arrived at odd expressions but too long ones) and it is complex for me... I would really appreciate your help.