Let $A$ be a PID, $A ⊂ R ⊂ A[x_1,x_2]$ with $R$ normal. Suppose that $x ∈ A$ and $R/xR$ is a domain. Is $R/xR$ normal? If not is there any condition on $R$ that will make this true?
Thank you.
2026-02-22 19:52:14.1771789934
Quotient of normal ring by principal ideal
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