Is there any example of this kind of rings? i don't have any imagine of this rings, if they are exist!
2026-04-01 16:44:17.1775061857
Example of the semisimple ring $R$ but $R^{{\rm op}}$ is not.
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By the Wedderburn-Artin theorem, a semisimple ring is a product of full matrix rings over division rings. Conversely, a product of simple artinian rings (like full matrix rings over division rings) is semisimple. This is left-right symmetric.