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:

    “Like sleep disturbances, some worries at separation can be expected in the second year. If you accept this, then you will avoid reacting to this anxiety as if it’s your fault. A mother who feels guilty will appear anxious to the child, as if to affirm the child’s anxiety. By contrast, a parent who understands that separation anxiety is normal is more likely to react in a way that soothes and reassures the child.”
    —Cathy Rindner Tempelsman (20th century)