Every field has an algebraic closure, and it is unique up to an isomorphism that fixes F.

It is the algebraic closure of the field of Laurent series.

There are several ways to represent the solution in an algebraic closure, which are discussed below.

Steinitz proved that every field has an algebraic closure.

Hence we consider an arbitrary field and its algebraic closure .

In algebra, the algebraic closure of a field.

In general, all algebraic closures of a field are isomorphic.

A special type also allows one to compute in the algebraic closure of a field.

These remain irreducible over an algebraic closure of the field.

The existence of an algebraic closure for a countable field (but not its uniqueness).