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.

Other articles related to "closure, normal closure, normal":

Conjugate Closure
... In group theory, the conjugate closure of a subset S of a group G is the subgroup of G generated by SG, i.e ... the closure of SG under the group operation, where SG is the conjugates of the elements of S SG = {g−1sg
Normal Extension - Normal Closure
... there is some algebraic extension M of L such that M is a normal extension of K ... such that the only subfield of M which contains L and which is a normal extension of K is M itself ... This extension is called the normal closure of the extension L of K ...

Famous quotes containing the word normal:

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