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I would like to know if the following is true.

Let $F$ be a field and let $p\in F[x]$ be a square-free polynomial. Then, the quotient ring $F[x,y]/\langle y^2-p\rangle$ is a UFD.

I am not sure how to approach this question.

Thanks!

  • 3
    If you suspect it's not a UFD, you might look for a non-unique factorization. Something, perhaps, like $y^2 = p$...2012-03-06
  • 0
    Yes, but I think it is a UFD. My problem is I do not know how to approach the problem. Thanks!2012-03-06
  • 0
    What makes you think it's a UFD?2012-03-06

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