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:

    “What strikes many twin researchers now is not how much identical twins are alike, but rather how different they are, given the same genetic makeup....Multiples don’t walk around in lockstep, talking in unison, thinking identical thoughts. The bond for normal twins, whether they are identical or fraternal, is based on how they, as individuals who are keenly aware of the differences between them, learn to relate to one another.”
    —Pamela Patrick Novotny (20th century)