asymptotics - Relatioship between the average of determinants of the following class of matrices and the determinant of the trivial one

ra.rings and algebras – Maximal orders separable over their centre Answer

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ra.rings and algebras – Maximal orders separable over their centre

Let $mathcal{A}$ breathe a central unostentatious $Okay$-algebra, the place $Okay$ is an algebraic quantity bailiwick. It is thought that $mathcal{A}$ is separable over $Okay$ (following the definition of DeMeyer and Ingraham’s bespeak). Moreover, it’s my judgement that an algebraic quantity bailiwick is separable over its ring of integers, so $mathcal{A}$ is separable over $mathcal{O}_K$, by transitivity of separability. My query issues maximal $mathcal{O}_K$-orders of $mathcal{A}$: are these separable $mathcal{O}_K$-algebras? If so, why? and if not, beneath what situations is an organize separable over $mathcal{O}_K$?

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