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A note on Non-Noetherian Cohen-Macaulay rings


Authors: Youngsu Kim and Andrew Walker
Journal: Proc. Amer. Math. Soc. 148 (2020), 1031-1042
MSC (2010): Primary 13H10
DOI: https://doi.org/10.1090/proc/14836
Published electronically: December 6, 2019
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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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Additional Information

Youngsu Kim
Affiliation: Department of Mathematics, University of Arkansas, Fayetteville, Arkansas 72701
Email: yk009@uark.edu

Andrew Walker
Affiliation: Department of Mathematics, College of Charleston, Charleston, South Carolina 29424
Address at time of publication: 2860 Seitzland Road, Glen Rock, Pennsylvania 17327
Email: walkeraj@cofc.edu, ajwalk010@gmail.com

DOI: https://doi.org/10.1090/proc/14836
Received by editor(s): January 10, 2019
Received by editor(s) in revised form: July 21, 2019
Published electronically: December 6, 2019
Additional Notes: The first author is the corresponding author.
Communicated by: Claudia Polini
Article copyright: © Copyright 2019 American Mathematical Society