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Sudhanshu Ranjan posted an Question
August 21, 2020 • 05:39 am 30 points
  • CSIR NET
  • Mathematical Sciences

Is q [x,y] principal ideal domain ?

is Q [x,y] principal ideal domain ?...........................

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  • Shashi ranjan sinha Best Answer

    We know that a polynomial ring F[x] is PID if and only if F is a field. Since Q[x] is just an integral domain, therefore Q[x][y] = Q [x,y] is not PID

  • Shashi ranjan sinha best-answer

    Considering your ring to be Q [x,y ] , I am giving you the solution. No, it is not PID.

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