Normal Closure

The term normal closure is used in two senses in mathematics:

  • In group theory, the normal closure of a subset of a group is the smallest normal subgroup that contains the subset; see conjugate closure.
  • In field theory, the normal closure of an algebraic extension F/K is an extension field L of F such that L/K is normal and L is minimal with this property. See normal extension.

Famous quotes containing the word normal:

    “Philosophically, incest asks a fundamental question of our shifting mores: not simply what is normal and what is deviant, but whether such a thing as deviance exists at all in human relationships if they seem satisfactory to those who share them.”
    —Elizabeth Janeway (b. 1913)