Page "Local field" Paragraph 1

Given such a field, an absolute value can be defined on it.

There are two basic types of local field: those in which the absolute value is archimedean and those in which it is not.

In the first case, one calls the local field an archimedean local field, in the second case, one calls it a non-archimedean local field.

Local fields arise naturally in number theory as completions of global fields.