Field extension of domain

Question

How can we say any integral domain has field extension?
How can we determine it?
For exapmle, If we take $\mathbb{Z}\subset \mathbb{C}$ as a integral domain. I would like to write elements of field extension of $\mathbb{Z}$.

Answer 1

Take a look at that : https://en.wikipedia.org/wiki/Field_of_fractions It's exactly what you're talking about.

It shows how, from an integral domain $R$, we can construct a filed $K$ "containing" $R$. $K$ is called the field of fractions of $R$.

Formally, it is the set $R \times R\setminus\{0\}$ quotiented by the equivalence relation $\sim$ defined by : $$(a, b) \sim (c, d) \iff ad = bc$$

In your case, the field of fractions of $\mathbb{Z}$ is $\mathbb{Q}$.