Separable Extension - Properties

Properties

  • If is an algebraic field extension, and if are separable over F, then and are separable over F. In particular, the set of all elements in E separable over F forms a field.
  • If is such that and are separable extensions, then is separable. Conversely, if is a separable algebraic extension, and if L is any intermediate field, then and are separable extensions.
  • If is a finite degree separable extension, then it has a primitive element; i.e., there exists with . This fact is also known as the primitive element theorem or Artin's theorem on primitive elements.

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