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:

    “I don’t mind saying in advance that in my opinion jealousy is normal and healthy. Jealousy arises out of the fact that children love. If they have no capacity to love, then they don’t show jealousy.”
    —D.W. Winnicott (20th century)