Correction to Problem 5 on the Obligatory assignment

There was an error in Problem 5 of the Obligatory assignment, the statement you were asked to prove in Part 1 is false in general without the additional assumption that the ring R be an integral domain. The problem set has now been updated in the .tex and .pdf files on the site. 

Thanks to Jan Meeus for pointing out the error. I apologise for the mistake. 

This exercise was an adaptation of Exercises 12 and 13 of Chapter 3 of Atiyah-Macdonald where the integral domain assumption was made at the beginning. It might be helpful to take a look at these exercises to get more intuition about torsion and torsion freeness. In particular Exercise 12 Part iii provides one route to prove the statement in part one. 

Do not hesitate to get in touch if you would like more hints or help with this or other problems.