If the localization $R_p$ of a ring $R$ at each prime ideal $p$ in A is Noetherian, does this imply that $A$ is Noetherian?
What we call such rings which is not Noetherian but localization at each prime ideal is Noetherian ?
Can somebody provide me any counterexample of (1) and also a good reference?
2026-03-26 20:44:14.1774557854
If the localization of a ring at each prime ideal is Noetherian, does this imply that ring is Noetherian?
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Consider the quotient of a polynomial ring in infinitely many variables with coefficients in a field by the ideal generated by all monomials of degree 2