I am attempting to follow the below solution for part (a) of Chapter 12, Problem M.7 in Artin's Algebra textbook. I am having trouble understanding why $\exists f_1,f_2\in M[f_1, f_2$ have no common factor].
By "common factor," I presume that this really means $\exists f_1,f_2\in M \forall d\in M$[$d|f_1$ & $d|f_2$ $\implies$ $d$ is a unit]. (Correct me if I am wrong.) But how would I go about proving that this is true?
