Question 8 (6 marks). A principal ideal domain (PID) is an integral domain R in which every ideal A is of the form A (a) = {ra | r = R} for some a Є R. (Recall that the = ideal (a) is called the principal ideal generated by a.) Suppose that R is a PID and A is a nontrivial prime ideal of R. Prove that A is a maximal ideal of R.