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I have some issues to prove that a certain ring is regular, and therefore to find a "general" method to do that. In order to exemplify, recently I was solving an exercice and one question was about regularity:

Let $A$ be a noetherian normal domain of dimension 1. Let $B=A[X]/(f(X))$ and assume that $B$ is a domain. Let $Q$ be a prime ideal of B contained in $g^{-1}(m)$ for $m$ maximal ideal of $A$. Find necessary and sufficient conditions on $f(X)$ such that $B_Q$ is regular.

Any book reference would also help a lot since I didn't find what I'm looking for yet

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    What is $g$ or $g^{-1}$? – 2017-01-25
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    A "noetherian normal domain of dimension 1" is often called a Dedekind domain. – 2017-01-25

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