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for the reasoning).
* Every localization of a commutative Noetherian ring is Noetherian.
* A consequence of the Akizuki-Hopkins-Levitzki theorem is that every left Artinian ring is left Noetherian. Another consequence is that a left Artinian ring is right Noetherian if and only if it is right Artinian. The analogous statements with "right" and "left" interchanged are also true.
* A left Noetherian

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