Chapter 5.4, Problem 14E

a. If $D$ is an ordered integral domain, prove that each element in the quotient field $Q$ of $D$ can be written in the form $\left[a,b\right]$ with $b>0$ in $D$.

b. If $\left[a,b\right]\in Q$ with $b>0$ in $D$, prove that $\left[a,b\right]\in Q^{+}$ if and only if $a>0$ in $D$.