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Are there properties of rings of which one does not know whether they are Morita or derived invariances?

For a recent such example for Morita invariance, see https://www.sciencedirect.com/science/article/pii/S0021869314004669 .

One can restrict also to special classes of rings such as finite dimensional algebras.

For derived equivalences it is for example an open problem whether having infinite dominant dimension is a derived invariant, see https://link.springer.com/article/10.1007/s11856-016-1327-4 .

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  • $\begingroup$ Certainly "yes" but your real question is "what are the unknown ones" right? $\endgroup$ – rschwieb Jun 28 at 13:21
  • $\begingroup$ Interesting related reading: mathoverflow.net/q/124856/19965 $\endgroup$ – rschwieb Jun 28 at 13:25
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    $\begingroup$ I remember reading in Carl Faith's books that it is unknown if the Ore condition is Morita invariant, but those books are pretty old. I haven't found anything about a resolution to it yet. $\endgroup$ – rschwieb Jun 28 at 13:25
  • $\begingroup$ @rschwieb Yes, I ask about the unknown ones. $\endgroup$ – Mare Jun 28 at 13:54

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