Over any algebraically closed field, there is just one Albert algebra.

Over an algebraically closed field it is equivalent to diagonalizable.

These conditions are equivalent over an algebraically closed field of characteristic zero, such as the complex numbers.

Because of this fact, C is called an algebraically closed field.

Any extension of an algebraically closed field is weakly C.

The absolute Galois group of an algebraically closed field is trivial.

Let C be an algebraically closed field and x a variable.

Let G now be a connected reductive group over an algebraically closed field.

The real numbers are not, however, an algebraically closed field.

Any extension of an algebraically closed field is regular.