35
$\begingroup$

In commutative rings we have the following

Theorem. $R$ is Noetherian if and only if each prime ideal of $R$ is finitely generated.

From this Theorem I am looking for commutative rings $R$ in which every maximal ideal is finitely generated but $R$ is non Noetherian.

Question: Is there a straightforward example of a commutative ring $R$ so that each maximal ideal is finitely generated, but $R$ is non Noetherian?

Thank You

4 Answers 4