Ravi posted an Question
July 26, 2020 • 02:34 am 30 points
  • CSIR NET
  • Mathematical Sciences

Is quadratic extension of a field necessarily seperable?

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  • Shashi ranjan sinha

    Quadratic extensions of a field F of characteristic not equals to 2 is always separable

  • Shashi ranjan sinha Best Answer

    Consider the polynomial x²-t in F[x], where F is the field of fraction of the polynomial ring over the field Z2 with indeterminate t

  • Shashi ranjan sinha best-answer

    No, it isn't necessarily separable. Quadratic extensions of a field of characteristic 2 may be inseperable.

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