Exercise 15, § 2

a) Let A be a principal ideal domain, let M be a divisible A-module (Ex. 3), and let N be a torsion A-module. Show that $M \otimes_A N = 0$. b) Let M and N be two $\tau$-primary modules with no elements of infinite height; show that $M \otimes_A N$ is a direct sum of cyclic submodules (use a) and Ex. 10, a)).