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!
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!