Morita invariant

Summary

A Morita invariant is a property of rings, or an object attached to rings, that is the same for any two Morita equivalent rings. Properties defined through the category of modules are Morita invariant, such as being semisimple, left Artinian or left Noetherian. Properties defined through elements, such as commutativity or having no zero divisors, are usually not. Morita invariants let one replace a ring by a simpler equivalent one, such as $M_n(R)$ by $R$.