Homework 2 corrections

Question 1.

$(a)\Rightarrow (b)$ is fine.

but $(b)\Rightarrow (a)$ should be modified to:

if $R^n\stackrel{f}{\to }R\to 0$ is an exact sequence then $f$ is given by a unimodular row.

The simple example that makes statement of $(b)\Rightarrow (a)$ false is :

$0\to \mathbb{\mathbb{Z}}\stackrel{\times 2}{\to }\mathbb{\mathbb{Z}}$