separable

comparative more separable · superlative most separable

1. Able to be separated.
2. mathematicsAble 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. mathematical analysisHaving a countable dense subset.
4. Any of several technical senses relating to the behavior of polynomials or objects over which polynomials can be defined:
   1. algebraHaving no repeated roots (where roots are considered in an algebraic closure)

      x²#43;1 is separable, since its roots are i and -i.

   2. obsoleteGalois theoryalgebraSuch that none of the irreducible factors of P have a repeated root.
   3. Galois theoryalgebraSuch that the minimal polynomial of every element of E is a separable polynomial.
   4. abstractalgebraSatisfying any of several technical conditions on the center of the algebra which generalize the situation of field extensions; see Separable algebra on Wikipedia.Wikipedia