Let $\mathcal{A}$ be a central simple $K$-algebra, where $K$ is an algebraic number field. It is known that $\mathcal{A}$ is separable over $K$ (following the definition of DeMeyer and Ingraham's book). Moreover, it is my understanding that an algebraic number field is separable over its ring of integers, so $\mathcal{A}$ is separable over $\mathcal{O}_K$, by transitivity of separability. My question concerns maximal $\mathcal{O}_K$-orders of $\mathcal{A}$: are these separable $\mathcal{O}_K$-algebras? If so, why? and if not, under what conditions is an order separable over $\mathcal{O}_K$?



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