Question

Let l be the set of elements of T whose numerators are divisible by $p$.

Prove that l is an ideal in T.

Short answer

It is proved that, l is an ideal by theorem 6.2.

Step-by-step solution

Obtain that  l is an ideal

Remember that $\left(p\right)\subseteq I$.

If $\frac{a}{b}\in T$for $k\in \mathrm{\mathbb{Z}}$.

It has$a=pk$and such that $\frac{a}{b}=p\frac{k}{b}\in \left(p\right)$

Hence $I=\left(p\right)$

Use theorem 6.2

And by using theorem 6.2, l is an ideal.