Existence of a right adjoint to a functor

Question

I am recently studying some topics on Category Theory and I am stuck with the adjoint functors (in this moment I decided to join Math SX).
I already know how to find a left or right adjoint, if it exists (usual free constructions etc.), but I find it challenging to prove that such adjoint functor does not exist.

In this case, I am asked to prove that there is no right adjoint at the forgetful functor from the category of commutative rings with unity to rings:
$F: \;\bf{CommRings} \to \bf{Rings}$
I already know some theorems, that state the conditions for a functor to have an adjoint (preserves limits, there exists an initial object in a category... etc), but I find it extremely difficult to understand, let alone apply them.