Homework 2 corrections

Question 3.

$(a)\nRightarrow (b)~$ ===> So one needs to add more assumptions.

example. $(\mathbb {Z} \oplus \mathbb {Z} /2\mathbb {Z} )\otimes _{\mathbb {Z} }2\mathbb {Z} \simeq \mathbb {Z} ~$ but $\mathbb {Z} \oplus \mathbb {Z} /2\mathbb {Z} ~$ is not a projective $\mathbb {Z} ~$-module.

This question is the exercise 3.1 of the K-book chapter 1 on page 23, also look at pages 15-23 for the review of line bundles and the picard group.