separable

Adjective

1. Able to be separated.
2. 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.
3. Having a countable dense subset.
4. Any of several technical senses relating to the behavior of polynomials or objects over which polynomials can be defined:
   • x²#43;1 is separable, since its roots are i and -i.

   1. (of a polynomial) Having no repeated roots (where roots are considered in an algebraic closure)

   2. (of a polynomial) Having no repeated roots (where roots are considered in an algebraic closure)

      (Galois theory, obsolete, of a polynomial P) Such that none of the irreducible factors of P have a repeated root.

   3. (Galois theory, of an algebraic field extension E/F) Such that the minimal polynomial of every element of E is a separable polynomial.

   4. (abstract algebra, of an algebra over a ring) 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