separable

Able to be separated.

Able to be brought to a form where all occurrences of the dependent and the independent variable are on opposite sides of the equal sign.

Having a countable dense subset.

Having no repeated roots (where roots are considered in an algebraic closure)

Such that none of the irreducible factors of P have a repeated root.

Such that the minimal polynomial of every element of E is a separable polynomial.

Satisfying any of several technical conditions on the center of the algebra which generalize the situation of field extensions; see Separable algebra on Wikipedia.Wikipedia