Example of non-principal ideal of the quotient ring $R[x,y,z]/(xyz-1)$

Question

Suppose $R$ is an integral domain, $R[x,y,z]$ is polynomial ring over $R$, and $$Q=R[x,y,z]/(xyz-1)$$ is a quotient ring. How to prove, that $Q$ is not principal ideal ring? I was trying to compose an ideal that cannot be generated by one element, but fruitless yet.

Edit: I guess this fact could be proven without constructing non-principal ideal, but I'm mostly interested in a proof in which such construction is made.

Answer 1

Hint: $Q \simeq R[x,y]_{xy}$. Now try finding a non-principal ideal in $Q$, while recalling how ideals arise in localisations.