Set of all prime numbers $(P, |)$ (division operator as relation) is a poset. All elements are minimal element. In the same way all elements are maximal elements right? say m is maximal prime, then if m | p then p = m right?
But in class, professor told maximal elements are none(probably i might have understood wrongly or did something wrong). Please clarify
If your professor was indeed talking about the division operator on the set of prime numbers, then no prime number divides any other prime number, so every element of that set is both minimal and maximal and there's not much more to be said.
But I suspect that your professor, when making that statement about no maximal elements, was instead referring to the set of all natural numbers (or, perhaps, all integers). And indeed, no matter what natural number $n$ you pick, it is not maximal with respect to the division relation: certainly there exists a natural number $m \ne n$ such that $n$ divides $m$.