# Characterization of right noetherian rings

Here's a quick question on noetherian rings. I know that for a ring $R$, the following are equivalent.

• $R$ is left noetherian
• Every finitely generated left $R$-module is noetherian
• Every submodule of a finitely generated left $R$-module is finitely generated.

Is there a corresponding result with 'left' replaced by 'right' throughout?

-
I am guessing there is. The reason why I ask is that I'm not sure if the proof of the above result I read in Curtis and Reiner's book carries over to the right noetherian case. Regards –  user165614 Jul 26 at 14:34
A right module over $R$ can be considered as a left module over the opposite ring $R^{\mathrm{op}}$; a ring is right noetherian if and only if its opposite ring is left noetherian. Just if you want to be fussy. –  egreg Jul 26 at 14:39