A note on the global dimension of shifted orders

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On arxiv

I consider dominant dimension of an order over a Cohen-Macaulay local ring inside the category of centrally Cohen-Macaulay modules. This is an invariant that measures how far away from being a Gorenstein order a given order is. As an application, I show that a result of Pressland and Sauter in the case of finite dimensional algebras also work in this setting - the result is concerning the global dimension of the endomorphism ring of some tilting object in the category of Cohen-Macaulay modules.