Conductor (awaiting review)

The conductor $\mathfrak{f}_R$ of an order $R$ is the colon ideal $(R:\mathcal{O})$, where $\mathcal{O}$ is the maximal order. Recall that a maximal ideal $\mathfrak{m}$ of $R$ is non-invertible if and only if $\mathfrak{f}_R\subseteq \mathfrak{m}$.