A note on Non-Noetherian Cohen-Macaulay rings

Kim, Youngsu; Walker, Andrew

doi:10.1090/proc/14836

A note on Non-Noetherian Cohen-Macaulay rings
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by Youngsu Kim and Andrew Walker PDF

Proc. Amer. Math. Soc. 148 (2020), 1031-1042 Request permission

Abstract:

In this note, we study the Cohen-Macaulayness of non-Noetherian rings. We show that Hochster’s celebrated theorem that a finitely generated normal semigroup ring is Cohen-Macaulay does not extend to non-Noetherian rings. We also show that for any valuation domain $V$ of finite Krull dimension, $V[x]$ is Cohen-Macaulay in the sense of Hamilton-Marley.

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